Panoptic unlocks long gamma positions onchain

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Inherent deficiencies with liquidity provisioning (LP) on Automated Market Makers (AMMs), such as impermanent loss, are well-known to DeFi traders, despite not being recognized for the short optionality positions that they are. While many mechanisms have attempted to address such issues, Panoptic adopts a radically different and much more intuitive approach: enabling traders to go long on optionality in an environment where this trade would otherwise be impossible.

In the first article of this report series, we illustrated that Panoptions are structured as exotic options and present opportunities to capitalize on inefficiencies within AMM market microstructure. The contents of this report will be focused on empirically validating those opportunities – how the streaming premia (streamia) paid for Panoptions is often underpriced relative to an illustrative simulation of the profit-&-loss (PnL) of scalping the gamma of a long optionality/convexity position.

Uniswap functions as an incomplete options market by design, allowing a large supply of short optionality via liquidity provisioning without an easy way for traders to take exposure in the opposite direction. The resulting oversupply of short optionality positions leads to underpricing Uniswap LP positions relative to their exposure to realized volatility. In this report, we will pinpoint exactly how and why these incomplete market inefficiencies can be exploited through gamma scalping on Panoptic.

Uniswap lets traders be short convexity

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Uniswap (and other AMM) LP positions allow traders to deposit a pair of assets and earn a rolling fee (called streamia) that is based on the volume and frequency of trades that their capital facilitates. However, hedging the delta of an LP position comes at a cost: by being a buyer in a rally and a seller in a sell-off, an LP is naturally short convexity. If the delta risk is hedged by taking long or short positions in spot and adjusting them dynamically as the spot price changes, that convexity still poses a systematic cost to the hedged LP position, sometimes called “reverse gamma scalping.”

This means that a “delta-hedged” Uniswap LP position gives exposure to two cash flows, both of which are dependent on realized volatility (RV). In one, the LP pays a systematic cost in order to maintain their hedge against exposure to movements in the underlying exchange rate between the tokens in the pool, paying the so-called “reverse gamma scalping” rate. In the other, depositing liquidity in the pool allows the LP to collect the fees paid by traders utilizing the liquidity that they have deposited in the pool.

However, there is no reason to believe that the design of the AMM’s fee structure should match the reverse gamma scalping rate. The amount that an LP stands to collect from an AMM pool over any period is dependent on:

• the volume traded in the pool (Uniswap lists pools for most token pairs in 1bp, 5bps, and 30bps fee tiers)
• the liquidity deposited by other users (who are allocated shares of the total fees collected by the pool proportional to the size and effectiveness of their LP position)
• The nature of flow seen by the pool (retail price-takers tend to adjust the AMM price with more volatility and volume than price arbitrageurs).

The only common driver between the Uniswap trading fees and the cost to maintain a dynamic delta hedge is volume, and even that link is only indirect via its relationship to volatility. In fact, as we will show, there are many cases where the rate paid to an LP is drastically lower than the cost to maintain a delta-hedged position. For example, fees paid to LPs of the ETH-USDC 30bps Uniswap pool were up to 18% less than the cost of gamma-scalping their delta exposure from January 2024 to December 2025.

The design of Uniswap (and other AMM) LP positions means that users can only take one side of this trade – short convexity – by owning an LP position. As a result, LPs are only able to pay the expensive rate (reverse gamma scalping) and receive the (often lower) trading fees.

The lack of venues to trade the long convexity side leads to a systemic inefficiency that prevents LPs from being paid fairly. Two-sided markets enabling participation in long convexity positions are essential to correcting this inefficiency. A sample of this asymmetric dynamic at play is displayed in the below chart of illustrative PnL using theoretical mid prices, where a 46% loss is suffered when deploying a reverse gamma scalping strategy in the ETH-USDC 30bps pool from January 2024 to December 2025.

Do Uniswap LP fees compensate for short-convexity?

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To test the difference between the delta-hedging PnL and Uniswap fee, we simulated the performance of hedging a long perpetual call position across multiple Uniswap v3 pools, considering a range of fee tiers and token pairs.

Notes on the Simulation

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As shown in the previous report, long-optionality Panoption positions are created by borrowing and selling short an LP position, “inverting” the exposure to gamma of the LP position. Similarly, long perpetual call Panoption positions can be created by trading a long put and going long spot (an application of put-call parity), meaning that the gamma profile (and so delta-hedging) of a put Panoption is the same as a call Panoption. Thus, results for calls also generalize to puts, with results for short positions obtained by taking the negative of the corresponding long positions.

While Panoptions are perpetual, meaning that they do not expire, the curvature (or gamma) of the value profile can be controlled by changing the price range at which the trader is willing to provide liquidity for the underlying Uniswap LP position. Tighter price ranges correspond to shorter effective “tenors” with higher curvature, while longer tenors can be mimicked by wider price liquidity ranges. In a similar way, the delta of the Panoption at entry can be chosen by centering the price range around different strikes relative to the prevailing spot price. To see a fuller explanation of this effect, please refer to the previous article in this series or Guillaume Lambert’s Medium articles.

We simulated hedging the delta of the position at entry, and thereafter allowed it to vary within a small range around 0 as spot prices moved over time. When the delta of the Panoption crossed that threshold, the position was re-hedged by buying or selling the appropriate number of units of the underlying asset. We tested a range of delta thresholds and reported the best performing selections below.

The Uniswap V3 positions that underlie Panoption positions require specifying a price liquidity range (which Panoptic uses to create synthetic “strikes” and “tenors” of panoptions, as shown above). As a result, the gamma of the Panoption is zero above and below the price range, which no longer requires the hedge position to be adjusted further since its delta remains unchanged at zero, and consequently the gamma-hedging PnL also remains unchanged. Correspondingly, there is no fee paid to hold the long Panoption as the liquidity deployed on Uniswap is not used to facilitate trading.

As a result, we simulate “rebalancing” the Panoption by closing out the position once the spot price leaves the target price range, re-entering a new position centred on the new spot price, and hedging the delta of the newly opened position. Assuming that the position is well delta-hedged at the time of rebalancing and ignoring gas costs, this process should incur no change in PnL.

A long call position has positive gamma, which means that by dynamically delta-hedging the Panoption, the trader receives a profit. That cost is weighed against the streamia paid continuously to hold the call Panoption. The chart below shows the theoretical performance of this process for a long 50-delta weekly Panoption in the ETH-USDC 5bps tier pool between 2024 and 2025. The delta was allowed to range between -5 and 5 before it was re-hedged.

In the chart above, the theoretical cumulative net PnL collected by the trader due this 5bps pool gamma scalping tactic largely exhibits a stable, “stairstep” pattern. Conversely, the ETH pool price endures massive fluctuations throughout the same sample period. This underlying turbulence is reflected in a buy-and-hold strategy within the ETH 5bps pool yielding only 31% returns while gamma scalping produces a lofty 219% return. In this simulation, gamma scalping provided a dual advantage through stability amid volatile market conditions as well as a demonstrable amplification in simulated profits.

The cumulative net simulated PnL of gamma scalping is arrived upon by deducting paid fees from the total raw payoff of the strategy. The two series are also highly correlated, as both are dependent on the RV of the spot price in the pool – whenever spot price moves, the delta of the position changes and requires an adjustment to the delta hedge. Similarly, price movements on other trading venues create arbitrage opportunities that drive trading activity in the Uniswap pool. These trades incur fees, which in the case of Panoptions are paid by the call option holder in the form of streamia.

Note that the two cashflows from hedging and streamia are different in two important ways. Firstly, the amount earned from gamma scalping is larger in almost all cases, resulting in a net profit across the full period. Secondly, the two series need not move at the same time. Owing to the fact that the number of units of spot in the delta hedge position is only updated when the absolute value of the delta moves above a given threshold, the capture of realized volatility is not perfect – spot may move around within the delta threshold bands without ever once breaching the bands and locking in hedging profits. However, the streamia fees paid to hold the long position are collected per-trade, meaning that every movement of spot adds to the streamia cost.

The Impact of Fee Tiers on Volatility

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Uniswap hosts trading pools for many assets across three different fee tiers (usually 1bp, 5bps, and 30bps of trade notional). As a result, the fees collected by LPs (and thus paid as streamia by long Panoption positions) are of a different magnitude. However, the fee tier also impacts pool fees through its effect on trade size and frequency.

Here, we replicate the analysis of the ETH-USDC pool as before (which one may naively expect to have the same volatility profile) to illustrate this effect. In this analysis the thresholds are broadened to an absolute of 15 delta to maximize the revenue of a call option in the ETH-USDC 30bps pool (as opposed to the 5-delta bands that were most profitable in the 5bps pool simulation).

The simulated performance is similarly positive (the simulated gamma scalping returns outweigh the relatively paltry recorded streamia fee collected by Uniswap LPs), but at a lower magnitude. The gamma scalping returns amounted to around 46%, while the buy-and-hold returns of ETH within the 30bps pool were 28%.

The reason for this disparity is simple: the price quoted by the 5bps pool is more volatile than that of the 30bps pool, requiring a more frequent delta hedge. As an example, the ETH-USDC 30bps call has a maximum of only 37 intraday hedges (albeit at larger sizes at the wider 15 delta bands), while the ETH-USDC 5bps call recorded up to 493 per day.

Below is a summary of the hypothetical annualized returns to gamma scalping using various delta thresholds in both the ETH/USDC 5bps and 30bps pools.

Under-supply of LP positions means that long convexity is more expensive

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The result is not unique to only high volume pools. The simulation run on WBTC-USDC 30bps pool also shows the same result for gamma scalping a 10-delta monthly call Panoption, but for a markedly different reason.

The chart above shows a net positive performance due to several “jumps” in hedging returns, despite the cost of streamia outweighing hedging profits over much of the sample period. Further examination of the data reveals that these large jumps in PnL are caused by large, volatile moves resulting in up to 66 hedges performed in a single day.

In contrast to the prior examples, the buy-and-hold return for BTC substantially outperformed the gamma-scalping return of 12% in the 30 bps pool. Simply holding WBTC over the same sample period yields a 105% return. This outcome illustrates the relationship between the supply of short-convexity through Uniswap LP positions and the effective “pricing” of volatility exposure.

ETH–USDC pools are among the most liquid AMM pools, with a large number of LP positions supplying liquidity. WBTC pools had relatively lower LP participation, resulting in a lower supply of short-convexity and higher streamia cost to the Panoption holder.

Gamma-scalping altcoins

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Uniswap’s AMM design supports trading pools for a wide range of token pairs. As a result, Panoptic’s infrastructure enables options trading on base–quote pairs that are not typically supported for trading on many other DEXs or CEXs, including memecoins.

This means traders can take onchain, long-optionality positions on tokens such as Shiba Inu (SHIB), PEPE, and Uniswap (UNI). We repeat the gamma scalping simulations on the SHIB-ETH 30bps pool, which pairs the Shiba Inu memecoin against ETH. Here, we keep the delta threshold to trigger re-hedging at an absolute value of 5 delta.

A similar “stairstep” pattern on the gamma scalping PnL appears. Notably, the maximum number of intraday hedges over this sample period was 500 – a natural result of the high volatility of the SHIB-ETH price.

The two charts above compare the net returns from gamma scalping alongside the performance of the underlying spot price for the PEPE–ETH and UNI–ETH 30 bps pools. Monthly calls with delta bands of 5 and 20 were used for the PEPE–ETH and UNI–ETH pool, respectively. Gamma scalping in the PEPE–ETH pool produced a net return of 202%, while the UNI–ETH pool yielded a net return of 48% over the sample period. The longer-dated Panoption structure also resulted in fewer intraday hedges, with the maximum number of hedges in a single day being 126 for PEPE–ETH and 14 for UNI–ETH.

As highlighted by the above table, the versatile attractiveness of gamma scalping among these three pools is further exemplified over buying-and-holding these tokens. The advantage of gamma scalping over buying-and-holding is demonstrated to persist over a variety of token pairs and fee tiers.

LP fees can be charged without a chance to lock in gamma scalping PnL

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LP fees can be charged even without a corresponding opportunity to lock in gamma scalping profits. This phenomenon was observed in a scenario where a massive spike in streamia occurred despite the spot price, when viewed on an hourly chart, never moving into the LP position range. Consequently, there was no change in delta, and thus no gamma scalp was locked in for the LP on the hourly basis.

Further examination revealed an "intra-block" flash crash, where the spot price briefly traded back within the LP range and then returned above it before the end of the block. These trades within the range triggered the payment of fees on the long call Panoption, yet the rapid reversal meant no gamma-hedging was performed within the hour.

This highlights that Uniswap’s market structure is inherently different from conventional markets, meaning that there are unique features to AMMs like intra-block trades that impact the results of gamma-scalping.

Conclusion

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This report quantitatively demonstrates that the over-supply of Uniswap LP positions’ short optionality can be monetized through the purchase and dynamic hedging of Panoptic’s options infrastructure.

Across multiple pools and fee tiers, our empirical results support this mechanism, showing that gamma scalping can be economically viable rather than merely synthetically replicable. We find that the magnitude and persistence of this effect depend on fee tier, liquidity depth, realized volatility, and the temporal resolution of hedging and fee accrual.

Finally, we show that optimizing delta-hedging parameters enables gamma scalping profitability across a broad range of Uniswap pools, including higher-volatility and niche assets not typically supported for options trading by centralized venues such as Shiba Inu and PEPE. Panoptic’s upcoming V2 platform will make gamma scalping accessible in the convenient form of a perpetual option vault (POV). Future work in this report series will examine volatility surface calibration and the structural distinctions between Panoptions and vanilla options.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

This article was originally published by Block Scholes on August 20, 2025. We are republishing it here with permission for broader accessibility. You can view the original report here.

Perpetual Options

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What if options never expired? Perpetual options are a new financial primitive that behave like traditional options that are continuously rolled forward. Instead of expiring, they maintain a fixed time-to-expiry horizon, say 30 days, by automatically rolling each day. The key benefit of this structure is efficiency: unlike manual rolling, perpetual options avoid repeated transaction fees and bid-ask spreads, making them significantly cheaper to maintain over time. They exhibit similar exposures to those of a traditional option, while smoothing volatile, market-dependent upfront costs into a continuous funding rate.

One of the core advantages of perpetual options is the substantial reduction in gamma risk since expiration never occurs. Because the time to maturity remains constant, the sharp increase in gamma seen in traditional options near expiry, particularly the pin risk, is largely avoided.

However, gamma exposure is not eliminated entirely; directional convexity still exists and must be managed, especially in volatile markets. The cost to dynamically delta hedge perpetual options with short gamma must be weighed against the floating premium paid for a perpetual option, which is itself dependent on the realized volatility of the underlying asset. The difference between these two volatility-dependent cash flows may offer opportunities for capture.

The idea of perpetual option writing naturally emerges in DeFi through liquidity provisioning (LP) in Automated Market Makers (AMMs) like Uniswap. LP positions, when modeled correctly, closely resemble short perpetual options: LPs are short gamma, long theta, and earn fees over time. These positions are effectively rolled forward every 12 seconds, each Ethereum block, and the fees earned are constantly priced by the market.

Despite their structural similarity to options, most LPs don't realize they are engaged in passive options selling. They often lack the tools or awareness to evaluate whether the fees they collect adequately compensate for the risks they're taking. As a result, the implied funding rate in AMMs is often too low due to an oversupply of short perpetual options. Protocols like Panoptic allow users to take the other side of this trade, to "buy" perpetual options, capturing mispriced convexity and helping correct these persistent market inefficiencies.

This report is the first in a series of articles that explore how AMMs inadvertently created the perfect infrastructure for perpetual options. It begins by examining how LP positions function as short perpetual options before introducing Panoptions, Panoptic's implementation that makes these positions explicitly tradeable. We will then describe how Panoptions behave differently from vanilla options, particularly in their Greeks and pricing dynamics, and why these differences create unique opportunities. Finally, we demonstrate how Panoptions complete the AMM ecosystem. By enabling both sides of the volatility trade, they provide a mechanism to correct the systematic underpricing that has persisted since Uniswap AMMs first launched in 2018.

What are Perpetual Options?

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Perpetual options are akin to perpetual futures (an instrument made popular on crypto exchanges): the instruments offer synthetic, leveraged exposure to an underlying asset, the extra cost of exposure via a derivative is paid on a continuous basis over the lifetime of the position, and the burden of continually rolling contracts is alleviated. While the fee structure for perpetual futures is largely predicated on either positive or negative underlying sentiment, the premia of perpetual options are path-dependent, closely tied to the realized volatility of the underlying asset.

Despite their exotic nature, perpetual options positions have a much more straight-forward exposure to Gamma: constant over time. As a result, the impact of the option’s exposure to realized volatility is far clearer, meaning that scalping or reverse scalping gamma based on underlying price action does not depend on an exposure that increases as the contract approaches an expiry. Perpetual options have previously been compared to baskets of vanilla options with varying expiries – when considered as a basket of continuously rolled, 0 days-to-expiration (0DTE) options, the constant gamma exposure attribute of perpetual options becomes easier to see.

Panoptions are Panoptic’s implementation of perpetual options. A Panoption provides long or short exposure to a constant payoff curve with convex exposure to the exchange rate between an arbitrary pair of assets. Instead of paying a premium upfront (as with vanilla options), Panoptions are paid for continuously as a function of the amount of time that an underlying asset spends within a specified price range. As the exposure profile of the position is constant, the usual concepts familiar to vanilla options traders are reframed: gamma is constant as a function of time (if not of the underlying spot price), the position's value does not change over time due to theta decay, and implied volatility must be treated with some care.

What is a Panoption really?

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Panoptic’s implementation of perpetual options takes advantage of an inherent optionality found in the liquidity provider (LP) positions of onchain exchanges like Uniswap. While Uniswap allows liquidity providers (LPs) to earn yield on a portfolio of assets by facilitating onchain trades between them, the automated quoting of exchange rates results in the LPs being exposed to an embedded short-optionality position. Here, we describe how onchain Automated Market Makers (AMMs) like Uniswap are leveraged by Panoptic to create perpetual option positions.

Decentralized exchanges – How spot prices are quoted automatically

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Decentralized exchanges (DEXs) for spot trading are a key innovation in Decentralized Finance (DeFi), representing a significant proportion of transaction activity on leading blockchains like Ethereum and Solana. DEXs are able to automatically quote prices to swap between a pair of assets without human input (and hence without a central limit order book) using an Automated Market Maker (AMM).

The most popular AMMs (as measured by total trade volume) function as a pool of two (or more) assets to be traded against one another, where the exchange rate that is quoted by the pool is derived from the ratio of the two tokens held by the pool. Any trader that wants to buy token A and remove it from the pool must deposit an amount of token B that preserves the product of the reserves of the two assets. The amount of token B that must be supplied for each unit of token A removed is the resulting price quoted by the pool for the trade.

Small trades that remove a small amount of the reserves are quoted at a price that is close to the (instantaneous) gradient of the constant curve (in blue above). Larger trades that remove a large amount of token A from the pool require a larger number of B tokens per A token, resulting in a worse execution price for the buyer of token A.

Providing liquidity – Being the AMM

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As well as trading against the prices quoted by an AMM, users can deposit both tokens to the pool in order to act as the market maker that takes the other side of trades with the pool. To do so, they must supply both assets to the pool in the same proportion as the assets already held by the pool and, in return, receive a Liquidity Provider (LP) token. The LP token entitles the holder to redeem the two assets at any time – but not necessarily in the same ratio in which they initially deposited them.

Therefore the LP token represents a right to redeem a portfolio consisting of two assets, whose ratio is dependent on the prevailing exchange rate between the two tokens quoted by the AMM. As a result, the LP position’s total value has an embedded convexity profile.

‘Convexity', in this context, refers to how the value of the LP token changes in relation to price movements of the underlying assets. In simpler terms, the rate at which the LP token's value changes isn't constant; it can accelerate or decelerate as prices shift – leaving a trader more exposed to selloffs during a selloff, and less exposed to rallies during rallies. Positive convexity behaves inversely, and is generally an attractive property for a portfolio to have.

The AMM model discussed thus far consists of liquidity providers that facilitate trades across an infinite range of prices. This means that, at any particular range (even those where trades are less likely to occur), there is liquidity. Not only does this mean liquidity providers may execute trades at prices they are not willing to trade at, it is also capital inefficient – as liquidity is wasted at ranges where price takers themselves are unlikely to transact in.

Take the example of any dollar-pegged stablecoin – assuming the token maintains its peg to $1 at all times, having capital deployed at $10 is inefficient given that it is an unlikely quoted price. To solve this, newer iterations of AMMs (such as Uniswap v3 and later versions) allow liquidity providers to specify a finite range of prices at which they would like to deploy their liquidity.

Relating the range of prices to the gradient of the curve above, we see that providing liquidity between a finite range of prices is equivalent to translating the price curve to the axes so that the liquidity provided is active between two points on the curve only. At either extreme, where the spot price quoted by the pool is above or below the range of prices that a liquidity provider has agreed to trade in, the portfolio redeemable by the LP token consists entirely of token A or token B. In these price ranges, none of the liquidity deposited by the liquidity provider is used to facilitate the pool's trades and the portfolio’s composition is static as a function of the spot price.

When the price quoted by the pool is within the range agreed by the liquidity provider, the liquidity deposited by the provider is “used up” by the pool, and the assets deposited by the LP token holder are bought or sold incrementally as the exchange rate between the assets changes. The change in composition of the portfolio as a function of the exchange rates between the two constituent assets between them is the key source of convexity in an LP token position.

Embedded convexity – Option-like payoff

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Deploying liquidity in this manner is essentially creating a range order – the liquidity provided by the LP will be fully converted from one token in the pool to the other as price moves through their chosen tick range.

Let’s see the effect of that observation by evaluating the value of an LP token as a function of the change in spot price. In the chart below, we assume a liquidity provider has taken a position in an ETH-USDC AMM pool and is willing to facilitate trades between 1800 and 2200, at a prevailing spot price of 1600 USDC per ETH.

At entry, the spot price is below the lower bound of the price range, and the LP token is redeemable for a portfolio consisting of ETH only. As the ETH-USDC spot price moves closer towards (but does not touch) the lower bound of the liquidity provider’s chosen range, the value of the ETH-only portfolio changes linearly with the change in the exchange rate between the two tokens.

When the spot price rises above 1800, however, and therefore enters the liquidity provider’s chosen range, some of the LP’s ETH is converted into USDC (by traders utilising the liquidity deposited by the LP to execute trades against the LP). The value of the portfolio at this point has curvature, because the composition of the portfolio shifts into USDC at exactly the same time that ETH appreciates in value against USDC.

Then, as the spot price crosses above the upper bound of the range at 2200, the portfolio is converted entirely into USDC. The value of the LP token is constant for spot prices above the upper price range boundary of 2200. Here, the LP token is redeemable for USDC only, and so its value does not change as a function of the ETH-USDC spot price.

An interesting consequence of the design of the AMM LP position is that the value of the LP token as a function of ETH spot price varies in a similar manner to a short put options contract. When the range of prices chosen by the liquidity provider is very tight, the curvature of the value of the portfolio is much higher nearer to the range and zero outside of it, and the value of the portfolio as a function of spot price resembles the familiar “hockey-stick” payoff curve of a short put contract very close to expiry. When the range is wider, the curvature is less strong but applies over a much wider range, and the curve looks a lot closer to a put option further away from its expiry date.

An equivalent short call option position can be constructed if the user borrows ETH to create that position, by taking advantage of the put-call parity identity (where a short put and short stock position holds an equivalent pay off to a short call).

This observation is not merely a coincidence – providing liquidity to an AMM and allowing traders to trade against you is conceptually similar to selling an option. In the example explored above, the liquidity provider gives away the right for someone to buy ETH from them at a given price, just like selling a vanilla put option with a pre-determined strike.

Matching Streaming Premium to a More Familiar Setting

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Streamed Premiums are how Panoption traders pay for convexity

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The existence of a streamed premium (rather than a payment upfront) may sound counter-intuitive, but it matches a core tenet known to derivatives traders: positions with long convexity don’t come for free.

We’ve seen how LP positions have an inherently short gamma profile. We’ve also seen how Panoptic provides the infrastructure to trade and lend these positions freely, allowing traders to invert the gamma exposure in order to be long convexity (much like a vanilla call or put option). Finally, we saw that the streaming premia (“streamia”) paid by long holders of a Panoption is paid dynamically over the holding of the option depending on the time that price spends within the position’s range.

Therefore, while a Panoption’s accumulated fees are a function of the (somewhat arbitrary) parameters set by the underlying Uniswap pool as well as the liquidity that has been deposited at each price tick, it is most importantly a function of the delivered volatility.

More specifically it is a function of the volatility that gets delivered within the range held by the option – the more time that price spends within the range, the more fees that are paid by traders of the underlying AMM pool, and the higher the fee collected by the LP position.

Delta hedging a Panoption should cost the same as the accumulated streamia

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Recall the value of a short panoption position – the value of an LP position as a function of the underlying spot price. To hedge this position, a trader can take an offsetting position in the underlying asset in order to hedge their exposure. A long delta position (as shown in the ETH short put example below) would require the trader to short an amount of ETH in order to hedge against changes in the exchange rate between ETH and USD.

This is similar to reverse gamma scalping. However, appearances and analogies to a short put are once again deceiving – the delta profile is not equivalent to a vanilla short put position. The LP has a constant delta outside of the specified range: it is constantly one below the range, and constantly zero above it. Within the range, the delta varies continuously, but gamma does not vary smoothly. Instead the gamma profile is closer to an indicator function.

As with a vanilla option, dynamically rebalancing the delta of a short gamma position incurs a systematic cost to the trader. Intuitively, this is because the act of rebalancing the delta necessitates the trader to buy when prices are high (having accumulated a larger short delta position) and sell when prices are low (having accumulated a larger long delta position). The potential profitability of such a strategy rests on the collection of fees paid for theta being able to outweigh realized underlying price movements during a certain span. Changes in the exchange rate between the two underlying tokens change the exposure of the position to delta, and so any hedge must be rebalanced.

However, taking a short put position in this way on an AMM also allows the trader to collect the streamed premium – the net position of a short position and a dynamic delta hedge results in two cash flows:

• The trader pays delta hedging P&L
• The trader receives the streamed premia from trading activity within their range on an AMM

Both of which are a function of the volatility that is delivered by the spot price of the underlying in the range within specified by the LP position. The natural question then is “Do they match?”

For no arbitrage assumptions to hold, the systematic cost of delta hedging the LP position should match the fee accumulated by providing liquidity on the AMM as the trader (assuming a perfect hedge and no transaction fees) takes no risk. However, in practice it is not at all clear that the fee structure specified by AMMs should result in an LP position accruing the same value in fees as was spent on the dynamic delta hedge. In addition, the pathwise nature of both cashflows further complicates the calculation of the expected value of either of these rates.

Comparison to Black Scholes – Panoptions are not vanilla options, but they’re close

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We showed above that the value of an LP function varies continuously with the exchange rate between the two tokens, with the curvature of the payoff resembling a short put position with a time to expiry that depends on the width of the range of prices that the liquidity is deployed to.

However, there are several key differences between an LP position and a vanilla option that make the analogy to vanilla options imperfect:

• LP positions do not decay – While the value curve of an LP token looks like a short put option, this is only true instantaneously. As time ticks forward, the value of a vanilla put option will decrease (and its curvature will increase), but the value of the LP token remains constant, assuming spot price does not move.
• LP positions can be exercised at any time – Instead of selling the right to buy a token at a specific time in the future, liquidity provision positions can be exited at any time. This makes them closer to an american option, with a strong path dependency.
• LP positions do not receive a premium upfront – Despite inherently selling optionality by deploying liquidity, liquidity providers do not receive a premium upfront as a vanilla options seller would. Instead, liquidity providers collect a fee for every trade that their provided liquidity range facilitates via the AMM.

These differences mean that, while they appear similar, an LP token cannot be perfectly hedged using a static portfolio of vanilla options. Instead, Panoptions are a more unique instrument, with convex exposure to the underlying asset that is instantaneously close to that of an options contract, but whose Greeks do not change dynamically with time.

Streaming Premium – What is the relationship to Black Scholes?

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Just as the value of an LP position is analogous to the payoff of short perpetual puts, the fees collected by LP positions are analogous to the premium of a vanilla option. The premium Panoptic charges from buyers to sellers of Panoptions is called streaming premium or “streamia.”

Streamia collection is contingent on the amount of time that the underlying price remains between the lower and upper price range.

Considering that the payment of a Panoption’s premium is conditional on the spot price remaining within range, it is natural to ask, “How does streamia compare to the Black-Scholes computation of vanilla options premia?” The answer lies in the union between local to implied volatilities and path-dependency.

Local volatility constitutes the instantaneous volatility of an underlying at any given local point, while Black-Scholes implied volatility represents the average of all local volatilities for price paths from the current spot price to the strike price.

Where the Black-Scholes implied volatility and Panoption-specific implied volatility differ can be attributed to the Black-Scholes implied volatility being assigned to a market of multiple vanilla options, which exhibit a skew to the volatility smile that violates the Black-Scholes assumption of a single, constant volatility level. Yet, Panoptions are path-dependent exotic options with cumulative properties. Panoptions can naturally accumulate more premia than vanilla counterparts at various junctures based on a significant amount of time spent in-range, and Panoption can also conversely be much lower than that of vanillas when underlying price largely migrates out-of-range.

However, just as local volatilities over a certain range average to Black-Scholes implied volatility, streamia has been statistically shown to eventually converge with Black-Scholes premia in expectation estimates. It is the designed path-dependency of Panoptions at any given discrete point that causes a temporary disparity in implied volatility and resulting premia.

This accrual embedding can also be reflected in an elevated Panoption implied volatility relative to Black-Scholes implied volatility.

In practice, however, panoptions accumulate streamia and local volatilities over a single delivered price path of the underlying, rather than an average of them. The results can amount to Panoption streamia and implied volatility being multiples higher than observed with Black-Scholes. The same empirical testing has borne out that 16% of all streamia realized over a set of price paths would be twice as large as the Black-Scholes estimates of vanilla options premia.

Vanilla options of certain expiries could be traded to replicate a comparably fixed-width Panoption. For example, continually rolling 0-days-to-expiration (0DTE) vanilla options every 12 seconds (or every block) would maintain a static gamma and structurally equate to a fixed-width Panoption.

For the sake of context, the natural corollary of being short gamma with a short options position is to also be long theta. Another distinction between Panoptions and vanilla options though is that theta is accrued for short Panoption positions as opposed to short vanilla option positions. The variation of expected streamia for a short Panoption position is accordingly far more dispersed when a Panoption is held for a shorter period of time. It is the imbued “cumulative” property of Panoptions spanning across the components of premia, theta, implied volatility, etc., that truly distinguish this instrument from other forms of exotic options. Local volatilities, streamia, and theta all accumulate based on the amount of time that the underlying for a Panoption remains within a specified price range.

Panoptic provides infrastructure that enables trading of perpetual options positions

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Despite carrying an embedded optionality component, LP positions can only be taken with short optionality exposure. Being unable to buy optionality means that existing AMMs function as incomplete options markets. The Panoptic protocol expands the functionality of AMMs to enable the trading of LP positions in both directions: long and short.

Natively, LP positions only allow short optionality positions as the liquidity provider gives up the right to choose when to execute a trade to traders. By providing a market place to borrow (for a fee) and sell LP positions, Panoptic allows LP shares to be shorted to invert the exposure and attain long optionality. In addition, perpetual call options can be traded by borrowing the underlying asset to create the LP position by taking advantage of put-call parity.

Panoptic’s trading and market infrastructure then greatly widens the universe of derivatives strategies that are able to be deployed onchain, as LP shares can then be speculated upon and hedged. Panoptic also permits more direct speculation on the underlying through the coupling of long perpetual at-the-money call positions with short perpetual ATM put positions, generating a synthetic perpetual futures position. Those synthetic futures can then be traded against off- or on-chain perpetual swaps, or even against expirable futures to produce arbitrage opportunities.

As AMM LP positions empirically equate to short perpetual put options, these positions are inherently short convexity. Therefore, allowing traders to take long optionality positions as well as short means that LP positions can be used to trade volatility more efficiently, monetising on the difference between realized and implied volatility in vanilla options markets by taking offsetting positions in each market.

The protocol also completes an otherwise unbalanced market, which already expresses itself in inefficient market dynamics. If the underlying spot price of a hedged LP position drifts below the lower bound of its range, the LP is forced to rebalance their position by redeploying liquidity at another price range and selling more of the underlying asset. This leads to a feedback loop known as the “Uniswap Price Doom Loop”, where LPs naturally depress underlying token prices by their rebalancing asymmetries. Allowing positions to be taken long as well as short provides a balancing force as LPs can perform this action in reverse, instead of all in the same direction.

Therefore, the unique value proposition of Panoptions trading is the expansion of AMM market microstructure, combined with the enabling of an onchain, perpetual option market. The platform aims to serve as a gateway to a more complete access to an underlying options market that already exists onchain. The added availability of exotic options also offers exciting opportunities to replicate and hedge exposure using standardized, exchange-traded products.

We detailed in this report how Panoptions compare to vanilla options intuitively, but what about empirically? For the next installment in this series on the Panoptic protocol, we will quantitatively hash out how Panoptions can be statistically simulated and hedged in practice.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Introduction

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Perpetual options are a new class of financial instruments that extend the flexibility of traditional derivatives by removing fixed maturity. Unlike standard European or American options¹, perpetual options offer the holder indefinite exposure to an underlying asset or strategy, often in exchange for a continuous fee or funding rate.

The pricing of these options poses a unique challenge. Without an expiry, classical models such as Black-Scholes become structurally incompatible, requiring either re-interpretation or novel mathematical frameworks. At the same time, the growth of decentralized finance has created new constraints and opportunities: oracles may be unreliable, expiries may be inefficient, and liquidity provisioning may act as implicit option selling.

This paper presents a comparative study of five distinct pricing models for perpetual options, each with a different motivation, mathematical structure, and degree of compatibility with DeFi protocols. These include:

• Panoptic’s Streaming Theta Model, a DeFi-native framework where pricing emerges path-dependently from AMM mechanics.
• Paradigm’s Everlasting Options, which emulate Black-Scholes via perpetual funding rates.
• Sidani’s Probabilistic Expiry Model, which interprets perpetual options as distributions over standard options.
• Gapeev & Rodosthenous’ Compound Perpetuals, which solve optimal stopping problems for layered contracts.
• Grossinho et al.’s Nonlinear Volatility Model, which accounts for risk feedback by making volatility a function of gamma.

For each model, we provide both a rigorous mathematical explanation and an intuitive plain-language interpretation. Our goal is to distill the assumptions, mechanics, and tradeoffs of each framework, and then evaluate how each model fits into a future of fully on-chain, composable financial primitives.

Model I: Panoptic – Streaming Premium from On-Chain Liquidity

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Quantitative Explanation

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Panoptic introduces a DeFi-native pricing model for perpetual options, built entirely on-chain and without relying on oracles, expirations, or snapshots. Instead of computing a theoretical value, Panoptic derives the cost of an option from the time-weighted Uniswap v3 and v4 trading activity within a chosen liquidity range.

Core Assumptions:

• Options are perpetual and do not expire.
• No oracle or external volatility input is used.
• LPs implicitly write short options by supplying liquidity in specific tick ranges.
• Option holders pay a fee based on the time spent within the LP range and actual trading volume.

Streaming Premium Mechanism:

The core idea is that Uniswap LPs accumulate fees when the price stays near their tick range — especially when liquidity is concentrated, this payoff resembles short option exposure. Panoptic lets users take the long side by paying a fee proportional to:

Where:

• $S_t$ is the spot price of the underlying asset at time $t$, as observed directly from Uniswap v3 or v4 ticks.
• $L$ is the lower bound of the LP’s tick range (acts like the strike floor).
• $U$ is the upper bound of the LP’s tick range (acts like the strike ceiling).
• $T$ is the total duration of the option position (not expiry, but how long the trader holds the position).

The indicator function $\mathbb{1}_{\{S_t ∈ [L, U]\}}$ ensures that fees are only accrued while the spot price is within the specified LP range.

The protocol defines a function FeeRate based on:

• Tick spacing (width of range),
• Volume traded inside the range,
• Amount of base liquidity,

Theoretical Approximation via Theta Integration

​

While not used for computation, the protocol shows that in expectation:

This links Panoptic's emergent pricing to the classical Black-Scholes model offering a mathematical benchmark. Under diffusive price paths (e.g., GBM), Monte Carlo simulations show that this streaming premium distribution converges to the Black-Scholes option price in expectation, though with wide variance. Some options cost nearly zero, others exceed Black-Scholes pricing depending on path risk.

In fact, Panoptic doesn’t pre-price an option, it charges dynamically as market activity unfolds. When the price lingers near the strike, more fees accrue. If the market stays away, no cost is incurred. This turns options into a metered service rather than a prepaid contract. In short: users pay for realized risk, not theoretical exposure.

Key distinction:
Unlike oracle-driven models, Panoptic infers implied volatility and pricing directly from liquidity and volume. This makes it not only oracle-free but also inherently composable with any Uniswap v3 and v4-compatible asset.

Plain-Language Explanation

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Panoptic doesn’t try to predict how much an option is worth using a math formula. Instead, it lets the option's cost emerge from what actually happens on-chain.

Here’s the idea: when a trader wants to go long an option, they do it by entering a position that can cause losses to an LP, someone who provides liquidity in a specific price range on Uniswap v3 and v4. The closer the market price is to that range, the more risk the LP faces. So, Panoptic charges the trader a fee that depends on how long the price stays in that “danger zone.” The longer the price remains near the strike, the more fees accumulate. This is similar to how traditional options lose value over time (called theta), but in Panoptic, it’s not based on a formula, it’s based on real trading activity and liquidity movement.

This fee is charged continuously, block by block, and only while the price is inside the strike range. If the price moves away, the trader stops paying. That’s why Panoptic options feel more like a “metered service” than a fixed contract; you're paying rent only when your position is risky.

The protocol doesn’t use oracles or external pricing models. Instead, it relies entirely on Uniswap data: ticks, liquidity, and trading volume. This makes the system fully decentralized and resistant to manipulation.

Model II: Paradigm – Everlasting Options

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Quantitative Explanation

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Paradigm’s everlasting options are synthetic perpetual options priced through a continuous funding mechanism inspired by perpetual futures. The buyer gains ongoing exposure to a standard European option but pays a time-based fee that mimics the option's time decay.

This model was introduced by Dan Robinson and Sam Bankman-Fried in their 2021 paper “Everlasting Options”, published by Paradigm. It draws clear conceptual parallels with the perpetual futures model pioneered at FTX, where a funding rate aligns the market price with a theoretical anchor. Here, instead of mirroring an asset price, the goal is to synthetically replicate an option’s fair value using a perpetual mechanism.

Core Assumptions:

• The option has no expiry.
• A Black-Scholes model defines the “fair value” of the option.
• An oracle provides the real-time inputs (spot, volatility) for pricing.
• A funding rate is used to enforce convergence between market and model value.

Black-Scholes Foundation:
Let $C_{\text{BSM}}(S, K, \sigma, r, \tau)$ denote the price of a European option with some fixed reference maturity $\tau$ (for example 1 day). This value becomes the mark price:

Black–Scholes Pricing Formula Variables:

• $S$: the spot price of the underlying asset
• $K$: the strike price of the option
• $\sigma$: the implied volatility of the underlying asset
• $r$: the risk-free interest rate
• $\tau$: the reference expiry used for BSM anchoring (e.g., 1 day)

Funding Rate:
The buyer pays funding at each moment based on the BSM theta:

with theta defined as:

Market Dynamics:
The actual market price $V_{\text{mkt}}$ may differ from the theoretical $V_{\text{BSM}}$. This difference incentivizes arbitrage, creating a funding flow that realigns the two.

Trader Payoff:
The trader's delta-neutral payoff in the Paradigm model is given by:

Where:

• $\Pi$: the total value of the trader’s position over time (mark-to-market PnL)
• $q$: the quantity of options held by the trader (assumed delta-neutral)
• $\theta$: the Black–Scholes theta, representing time decay
• $V_{\text{mkt}}$: the actual market price of the perpetual option

This equation represents the rate of change of the trader’s profit over time when their position is hedged against movements in the underlying asset. The term $\theta$ accounts for the time decay of the option as defined in the Black-Scholes model, while $\frac{dV_{\text{mkt}}}{dt}$ captures the market-driven price change of the perpetual option. Together, they determine the trader’s net return per unit time in a funding-based system like Paradigm’s.

Liquidation:
Positions are margin-bound. If market losses or theta payments reduce collateral below the maintenance threshold, liquidation occurs just as in perp markets.

Interpretation:
This structure emulates option holding costs in a perpetual fashion. The holder pays the equivalent of daily theta decay to keep the position open, just as a perp trader pays funding. While elegant, this design assumes oracle accuracy, volatility stability, and a liquid hedging infrastructure which are requirements more natural to centralized venues than DeFi.

Key difference from Panoptic:
Panoptic embeds the same intuition — theta-based pricing — but derives it naturally from Uniswap v3 and v4 activity, without external data. Paradigm models decay; Panoptic observes and charges it.

Plain-Language Explanation

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Imagine you want to hold an option forever, but instead of paying everything upfront, you just pay a small “rent” every block. This rent reflects how much the option would normally decay over time in a standard pricing model like Black-Scholes.

Paradigm’s everlasting options are built exactly around this idea. They are inspired by perpetual futures contracts: just as a perp tracks an asset through a funding rate, the everlasting option tracks the value of a traditional option by charging a funding rate based on its time decay, or theta.

Each second, the protocol calculates what a normal short-term option would be worth and then charges or credits the trader accordingly. If the market price drifts too far from this “theoretical” value, arbitrageurs step in buying low and selling high which helps pull prices back in line.

But to make this work, the system depends heavily on oracles. It needs to know the live price of the asset and estimate volatility accurately. If the oracle is wrong, the whole pricing breaks down. This structure fits very well in centralized environments, where you can compute Black-Scholes precisely, but is more fragile in DeFi where data is fragmented or noisy.

Paradigm starts from a pricing model and builds a mechanism to match it pulling the market toward a Black-Scholes anchor. Panoptic does the opposite: it lets pricing emerge from how traders interact with the protocol, using streaming fees from LP positions. Paradigm needs an oracle; Panoptic doesn’t.

Model III: Sidani – Probabilistic Expiry via Option Mixtures

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Quantitative Explanation

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Sidani proposes a novel pricing model for perpetual options by treating them as an infinite series (or integral) of standard European options, each with a random expiry. Instead of assigning a fixed maturity, the perpetual option is valued as a probabilistic average over vanilla options drawn from an expiry distribution.

Model Setup: The perpetual option value is derived as the expected value of a European option whose expiry $T$ is drawn from a known probability distribution.

Step 1 – Discrete-Time Formulation:
The original form of the model is expressed as a discounted sum:

where:

• $\delta \in (0,1)$ is a constant reflecting the investor’s time preference or discount factor,
• $\lambda \in (0,1)$ is the decay parameter of the geometric distribution,
• $V_{\text{BSM}}(t)$ is the price of a vanilla European option with maturity $t$.

This expression represents a perpetual option as a portfolio of European options, where shorter expiries are more heavily weighted.

Step 2 – Probabilistic Interpretation:
Let $T \sim \text{Geo}(\lambda)$ be a random variable with:

Then, the perpetual option price becomes:

The use of $\delta^T$ inside the expectation reflects exponential discounting over time.

Step 3 – Continuous-Time Approximation:
For continuous maturity $T \sim \text{Exp}(\lambda)$, we obtain the integral form:

Interpretation of Parameters:

• $\lambda$ controls the shape of the distribution. A higher $\lambda$ implies shorter expected expiry $\mathbb{E}[T] = \frac{1}{\lambda}$.
• $\delta$ discounts future values and can be interpreted as a funding adjustment or time preference.

Connection to Funding Rate:
While this model does not directly use a funding rate like Paradigm, the decay of weight over time ($\lambda$) acts as a proxy for the economic cost of holding exposure; shorter expiries dominate because longer-term exposure is discounted.

Conclusion:
This formulation offers a mathematically clean, expectation-based pricing for perpetual options. It does not rely on path-dependence or external price oracles (unless $V_{\text{BSM}}$ needs to be fed via oracle). The model is intuitive, composable, and compatible with both analytical and Monte Carlo methods.

Plain-Language Explanation

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You can think of the Sidani model as a blend between uncertainty and flexibility. Since you don’t know when the option might mature, the model prices in a whole distribution of possible expiries. This adds a kind of “weighted imagination”, you imagine every possible European option across time and combine them. The result is a smooth, continuous valuation that reflects both short-term and long-term risk. It’s as if the market constantly rolls the dice on expiry and charges you based on the average cost of all those possible outcomes.

Sidani’s model answers a tricky question: “How do you price something that never expires?” Instead of trying to force-fit a formula, it says: what if we imagine the expiry is unknown like a spinning wheel that could land on 1 day, 10 days, or 100 days, but with shorter expiries more likely?

Then, we price a normal option (using the Black-Scholes model) for every possible expiry, and take the average weighted by how likely that expiry is. If short expiries are more likely, they get more weight. If we use an exponential curve, the price looks a lot like what you’d expect for a perpetual option.

This approach is clean, flexible, and easy to simulate. You can run a Monte Carlo with expiry drawn randomly, or integrate it analytically if you know your distribution.

Key difference from Panoptic:
Sidani mixes snapshots of standard options with different time horizons. Panoptic tracks the real path of the price over time and charges based on how long it stays risky. One uses a probabilistic mixture; the other uses a real-time stream.

Model IV: Gapeev & Rodosthenous – Compound Perpetual American Options

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Quantitative Explanation

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This model studies the valuation of compound perpetual American options, i.e., options whose underlying assets are themselves perpetual American options. These contracts involve a nested exercise structure, leading to a multi-layer optimal stopping problem under continuous-time diffusion models.

Contextual Note:
Although compound options differ from the other models in this paper: in that their underlying is itself an option rather than a spot asset, we include the Gapeev & Rodosthenous model to expand the conceptual boundaries of perpetual option pricing. By introducing perpetuality at multiple layers of optionality, this framework showcases how the perpetual structure can be embedded recursively. It provides a valuable theoretical benchmark and highlights the potential complexity and richness of derivative instruments when expiry is removed entirely.

Underlying Framework:

• The underlying asset $S_t$ follows a geometric Brownian motion with dividend yield $\delta$:
  $$dS_t = (r - \delta) S_t \, dt + \sigma S_t \, dB_t$$
  where:
  • $r$ is the risk-free interest rate.
  • $\delta$ is the dividend yield of the underlying asset.
  • $B_t$ is the standard Brownian motion.
• The option is perpetual and American-style: exercisable at any time, without expiration.
• The compound option payoff depends on the early exercise of an inner perpetual option.
• Closed-form solutions are derived using martingale methods and optimal stopping theory.

Compound Structures Analyzed:

• Call-on-Call: Right to buy a call option.
• Put-on-Call: Right to sell a call option.
• Call-on-Put: Right to buy a put option.
• Put-on-Put: Right to sell a put option.
• Chooser Option: Right to choose between a perpetual call or put at optimal exercise.

Each structure yields a different value function, depending on the composition of the inner and outer exercise rules. The general solution form for many of these contracts is:

Where:

• $\gamma_\pm = \frac{1}{2} - \frac{r - \delta}{\sigma^2} \pm \sqrt{ \left( \frac{1}{2} - \frac{r - \delta}{\sigma^2} \right)^2 + \frac{2r}{\sigma^2} }$
• $b^*$ is the critical exercise boundary for the outer option. Boundary refers to a critical price level of the spot asset at which it becomes optimal to exercise the option. In this model, it is a threshold value of the spot price $s$ (typically denoted $b^*$) that solves the optimal stopping problem.
• $A$ is chosen to satisfy value-matching and smooth-pasting conditions.
• $s$ is the spot price of the underlying asset (since the underlying asset is an option).

Example – Call-on-Call:
Let $K_2$ be the strike of the inner perpetual call and $K_1$ the cost to acquire it. The value function is:

with critical boundary:

Optimality Conditions:

• Martingale verification (Snell envelope)
• Value matching and smooth-pasting conditions
• Analytical solution of free-boundary PDEs

Interpretation:
Pricing a compound perpetual option requires identifying the optimal stopping time for both the outer and inner options. These solutions reflect both continuation and early exercise regions and give closed-form expressions for value and boundaries. This approach offers a rare, explicit benchmark for multi-layer optionality.

Plain-Language Explanation

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Imagine an option — but instead of giving you the right to buy an asset, it gives you the right to buy another option. That’s a compound option. It’s like financial nesting dolls: one option layered inside another. And in this case, both the inner and outer options are perpetual and American-style, meaning they can be exercised at any time and never expire.

Let’s walk through a concrete example: a call-on-call.

You pay a premium today for the right (at any point in the future) to purchase a perpetual call option on a stock. That inner call option also doesn’t expire and gives you the right to buy the stock. So you’re essentially buying optionality on optionality.

Now here's the tricky part: you want to exercise the outer option only if the inner one is worth it. That means you need to know:

• When is the inner option “in the money” enough?
• And how much value would be left after paying the outer strike?

The paper solves this problem by finding the optimal moment — or price level — at which it makes sense to pull the trigger. These price levels are called critical boundaries, and the math uses martingale theory and optimal stopping to calculate them.

The result is a set of clear formulas:

• If the asset price is below a certain boundary, you wait.
• If it's above, you exercise the outer option, claim the inner one, and then you're in the game.

Each compound structure — whether it’s a call-on-put, chooser, or put-on-call — has its own logic and boundary. But the idea is always the same: wait until it’s worth unlocking the next layer.

Key difference from Panoptic:
While Panoptic relies on continuous fee accrual driven by path-dependent Uniswap activity, the Gapeev & Rodosthenous model assumes no trading activity and instead solves for closed-form optimal exercise boundaries in a frictionless market. Panoptic options are paid as-you-go and can be held indefinitely, while this compound model requires an explicit stopping decision at well-defined price levels. Unlike Panoptic’s emergent pricing from market mechanics, this model is fully analytical and assumes complete market observability.

Model V: Nonlinear Volatility in Perpetual American Put Options (Grossinho, Faghan, & Ševčovič, 2017)

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Quantitative Explanation

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This model extends the classical Black-Scholes framework for pricing perpetual American put options by allowing the volatility function $\sigma$ to depend nonlinearly on the second derivative (Gamma) of the option price.

Variable Definitions for Grossinho et al. Model

• $S$ is the spot price of the underlying asset.
• $V$ is the value of the perpetual American put option.
• $SV$ is the shorthand notation for the second derivative of $V$ with respect to $S$, i.e., the option’s gamma: $SV = \frac{d^2V}{dS^2}$.
• $\rho$ is the feedback parameter that scales how volatility responds to the option’s convexity (gamma).
• $r$ is the risk-free interest rate.
• $E$ is the strike price of the put option.
• $\sigma_0$ is the base level (unperturbed) volatility when feedback is zero.
• $H$ is the optimal exercise boundary; the critical spot price below which it becomes optimal to exercise the option.

Core Setup:

• Underlying follows a geometric Brownian motion.
• Option is perpetual and American-style.
• Volatility is state-dependent: $\sigma = \sigma(S, H)$ with $H = S V''(S)$.

The resulting nonlinear PDE for the option value $V(S)$, valid for $S > \rho$, is:

with early exercise boundary conditions:

Example Nonlinear Volatility Form:

where $\lambda$ is a sensitivity parameter capturing feedback effects from Gamma.

Classical Case (Merton):
When $\sigma \equiv \sigma_0$ is constant, the closed-form solution reduces to:

Methodology:

• Existence and uniqueness of a solution for general $\sigma(H)$
• An implicit equation for the free-boundary $\rho$
• Numerical solutions for the option value and stopping region

Plain-Language Explanation

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This model tweaks a standard perpetual put by making volatility respond to risk.

Think of it like this: if the option value changes rapidly with price (i.e., high Gamma), the market becomes more volatile. This might reflect increased trading friction, hedging demand, or liquidity sensitivity.

So instead of assuming fixed volatility, the model lets it grow when the option is “more dangerous.”

You still get a critical price $\rho$: below it, you’d exercise the put immediately. Above it, you wait. But now this boundary depends on more complex market dynamics.

If there’s no feedback (i.e., $\lambda = 0$), the solution becomes the classical Merton perpetual put. But when feedback is present, the exercise region can shift wider or narrower depending on how reactive volatility is.

Why it matters:
This model adds realism by accounting for nonlinear effects. It is useful in illiquid markets or protocols with reflexive price behavior.

Relation to Other Models:
While Paradigm and Sidani use static volatility and external pricing, this model is internally dynamic. It doesn’t require an oracle; but it also doesn’t yet fit natively in DeFi. Still, it shows how feedback pricing could inspire future mechanism design in protocols.

Important Question: Why is most perpetual option research focused on American-style options?

Because American-style options are inherently tied to optimal stopping problems, they remain meaningful even when there is no expiry. European options with no expiry don’t make much sense. In fact, if you can only exercise at $T = \infty$, you never actually receive a payoff.

Thus, a perpetual European option is often considered trivial or degenerate. American options, by contrast, give the holder the right to choose when to exercise. When the expiry is removed, the problem becomes:

“What is the optimal price level at which to exercise, regardless of how long it takes to reach it?”

This setup leads to mathematically rich free-boundary problems, which can be analyzed and solved using tools from optimal stopping theory.

Summary Comparative Table

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Conclusion

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Perpetual options represent more than an innovation in pricing, they signal a shift in how we design financial primitives. Without expiry, the boundaries of flexibility, composability, and on-chain autonomy expand. The challenge is no longer how to replicate Wall Street on-chain, but how to invent new forms of risk, flow, and strategy that are native to decentralized markets. Pricing becomes a question of incentive alignment, liquidity behavior, and protocol dynamics. As the ecosystem evolves, perpetual options may power the next generation of credit, leverage, insurance, and structured products; all live, modular, and governed by code. The future of derivatives is not just continuous. It is programmable.

References

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• Panoptic Protocol Team
  Panoptic Whitepaper v1.3.1. Published in 2023.
  https://docs.panoptic.xyz/

• Dan Robinson and Sam Bankman-Fried
  Everlasting Options. Paradigm Research, 2021.
  https://www.paradigm.xyz/2021/05/everlasting-options

• Sidani, W.
  Pricing Perpetual Options Using a Distribution over Expiry.
  (Private draft/notes, circulated in DeFi research community), 2023. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5065014

• Gapeev, P. V., and Rodosthenous, N.
  Perpetual American Compound Option Valuation.
  Quantitative Finance, Volume 13, Issue 1, 2013, pp. 129–139.
  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1698264

• Grossinho, M. R., Faghan, M., and Ševčovič, D.
  Pricing Perpetual Put Options by the Black–Scholes Equation with a Nonlinear Volatility Function.
  arXiv preprint arXiv:1611.00885, 2017.
  https://arxiv.org/abs/1611.00885

• Ekström, E., and Lu, B.
  Perpetual American Options with Stochastic Volatility.
  Mathematical Finance, Volume 31, Issue 2, 2021, pp. 757–785.
  https://doi.org/10.1111/mafi.12271

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Feel free to check out our livestream video on YouTube!

An underdeveloped area of research within traditional markets is how futures term structure interacts with and can precipitate underlying volatility. Contango characterizes an upward-sloping futures term structure where spot trades at a discount to futures prices, while backwardation characterizes a downward-sloping futures term structure where spot trades at a premium to futures prices. Both term structure regimes entail an eventual convergence to the spot price with contangoed futures declining and backwardated futures rising at expiration as the below graphic conveys. We will pinpoint exactly how excess volatility can be a byproduct of extremal points in the futures term structure, how these futures polarities coincide with underlying spot prices as well as the implied components of options markets, and how these properties can be collectively harnessed and capitalized upon through Panoptions trading.

Prior studies have demonstrated how price volatility displays a “V-shaped” pattern in relation to the extremes of a futures term structure. The below visual portrays this smile-like trend in the case of crude oil. Acute backwardation signals an increased desire to hold an underlying asset due to a high convenience yield and depressed levels of physical storage, thereby propping up spot prices to trade at a premium to futures prices. The opposite mechanics occur when detailing the origins of severe contango. There is an inverse correlation between the convenience yield and physical storage whereby when the convenience yield for a commodity is high (low), there is a connotation that physical storage is low (high). This conventional interrelationship in commodities does not hold when applied to crypto though, which we will detail later in this article.

Since frenetic activity in the futures term structure is primarily reflected through underlying realized volatility (RV), we employ a statistical barometer such as the variance risk premium (VRP) to gauge how RV moves in concert with the options lens of implied volatility (IV) by deducting implied variance from realized variance to compute the VRP as shown in the below formula. The VRP bears a key distinction as a metric from the volatility risk premium in that it permits the IV for every strike on an options chain to be encapsulated rather than the IV at a single strike price, so we elected to feature the VRP in our analysis due to its all-encompassing potency in quantifying the evolution of RV-IV dynamics.

$VRP_{t,T} = N * [RV_{t,T}^2 - IV_{t,T}^2]$

where $N$ is a notional amount, $RV$ is realized volatility, and $IV$ is implied volatility.

Although, the VRP cannot explain futures returns in a state of either heightened contango or backwardation. We accordingly chose to further deconstruct the realized variance component of the VRP into the semi-volatilities of upside and downside RV by calculating volatility realized for simple positive underlying returns (r>0) or simple negative underlying returns (r<0) respectively. But a question remains as to whether upside or downside RV accounts for a larger proportion of overall realized variance? How can this line of inquiry be resolved with the added dimension of underlying spot movement? The answer lies in the degree of volatility clustering for either realized semi-volatility.

Volatility clustering is a well-established empirical trait observed with movements in financial time series where large returns of either direction tend to follow large returns, small returns tend to follow small returns, etc. This property effectively expresses the extent to which volatility persists or autocorrelates (i.e. “clusters”) during a given period. Disaggregating the persistence of the upside and downside realized semi-volatility will permit us to analyze which types of returns (positive or negative) contribute more to a realized variance spike within a regime of elevated contango or backwardation. Within the prism of the VRP, the question then becomes how does IV move in relation to RV amid these spikes?

The scope of this article will interweave three separate conceptual arenas in futures term structure, the VRP, and volatility clustering to supply differentiated insights. The indicators that we explore will outline how to time and execute certain onchain options strategies when futures markets are in flux. RV dynamics can be truly distinct from IV dynamics, but we will lay out the steps as to how to capture the differential between the two through trading volatility on Panoptic. We will also be commentating on why embedded cyclicality tied to the three variables in our analyses are unique to crypto volatility markets.

Results

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As Panoptic is a perpetual options trading platform, the backtests that were deployed on the ETH/USDC and WBTC/USDC 30bps Uniswap pools to assess dated or expirable futures market activity were specifically adjusted through the filter of perpetual futures (perps) by way of trading synthetic perps (see code here). A long synthetic perp position is formed by coupling a long At-The-Money (ATM) 50-delta Panoption call with a short 50-delta Panoption put. While conventional perps would entail long positions paying a funding rate to short positions during contango and vice versa during backwardation, long synthetic perp positions on Panoptic will accrue outsized positive returns amid contango and outsized negative returns (positive returns for short synthetic perp positions) amid backwardation.

We utilize Panoptic-native synthetic perps returns as proxies for contango and backwardation due to the BTC trend depicted by the above figure. The chart reveals how the BTC funding rate derived from various centralized exchanges (CEXs) changes in accordance with the underlying BTC price. This illustration demonstrates how underlying BTC price tends to increase (decrease) alongside CEX BTC funding rate increases (decreases), indicating that severe perp funding rate contango (backwardation) would serve as an adjunct to steep price increases (decreases). Hence, we transpose this logic concerning perp-price interdynamics offchain to our synthetic perps trading onchain.

The above graphic reveals the long synthetic perp monthly backtest results on the ETH/USDC 30bps pool for a sample period spanning from May 2021 through June 2025. The maximum monthly return of 56.7% (21867% annualized) for the position was attained in July 2022 with the largest gain of 44.4% (8133%) for a short synthetic perp position being realized during the immediately prior month of June 2022. Assuming a persistent positive correlation between underlying prices and perp funding rates, we extrapolate that this ETH pool was likely under contango in July 2022 and backwardation in June 2022. We can thus proceed with looking to identify how the VRP and certain directional volatility persistence present themselves and accompany magnified contango and backwardation during these pressurized periods.

The above visualizations unveil results concerning the 30-day rolling VRP, spot-RV correlation (correlation between simple spot returns and RV), and semi-volatility persistence over the course of the previously mentioned sample period. We parametrize volatility persistence by virtue of the Hurst exponent. The Hurst exponent is a metric designed to quantify the degree of autocorrelation or trendiness within a time series. A Hurst exponent on RV greater than 0.5 is indicative of elevated volatility clustering with a value less than 0.5 signifying subdued volatility clustering, while RV that generates a value around 0.5 is deemed to be governed by a purely stochastic process.

Rises in the VRP predominantly coincide with increases in spot-RV correlation, which is further statistically supported by synchronized timing with heightened upside realized volatility persistence. Conversely, declines in the VRP largely align with decreases in spot-RV correlation and intensified downside realized volatility persistence. The most sweeping interpretation that can be discerned from this suite of analytics is that contango for the pool primarily transpires in conjunction with an augmented VRP-upside volatility persistence regime, whereas backwardation occurs alongside the opposite state with diminished VRP and enhanced downside volatility persistence. Intuitively, we are then incentivized to long (short) underlying ETH through spot, perps, expirable futures, synthetic perps, etc., as early-stage contango (backwardation) deepens.

The same synthetic perp backtest was conducted on the WBTC/USDC 30bps pool during an identical sample. Although the maximized returns for long and short BTC synthetic perps are not as great in absolute terms as ETH, the largest gain for the BTC long synthetic perp position outweighs the largest gain for the short synthetic perp position, which is observed as being the case with ETH as well. The top monthly return for the long BTC synthetic perp position was 43.8% (7732% annualized), and the top monthly return for the short BTC synthetic perp position was 37.1% (4317% annualized). With the same assumptions as before, we extrapolate that this Bitcoin pool was likely under contango in February 2024 and backwardation in June 2022. Once again, we go on looking to identify the same technical markers as we did with ETH.

Also akin to ETH, there is a nexus between the BTC VRP and directional volatility persistence, but it does not appear to be as pronounced until the onset of 2023. When taking stock of both ETH and BTC pools, there is a clear asymmetry with regard to increased upside volatility clustering contributing to overall realized variance spikes disproportionately more than increased downside volatility clustering. A defined void has been illustrated between the severe contango-expanded VRP-bolstered upside volatility clustering linkage versus the severe backwardation-reduced VRP-concentrated downside volatility clustering paradigm. In both pools, the most direct trading synopsis is to directionally long (short) the underlying through whatever directional means as contango (backwardation) is sharpened during nascent phases. But this perspective begs the question from an implied standpoint as to how we can trade the market if either underlying contango or backwardation has seemed to have already reached a local summit?

Broader Discussion & Conclusions

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Despite there being a demonstrably asymmetric impact of upside RV on enlarging the VRP for both ETH and BTC, the inverse dynamic prevails concerning implied variance. The VRP for both assets diminishes in the wake of rising downside volatility persistence, meaning that implied variance overwhelms realized variance in the midst of falling markets. Downside volatility skew thereby dominates the implied variance component of the VRP, firmly contrasting with upside volatility reigning quantitatively supreme over the VRP realized variance segment. What explanation lies at the base of this major realized-implied divergence? We contend that the root of such a marked bifurcation is predicated on the downwardly-biased feedback loop that is the crypto-native convenience yield.

In commodities markets, the convenience yield measures the benefit of holding a physical commodity rather than futures contracts, particularly during shortages. Swings in physical storage are what principally dictate futures term structure in TradFi commodities as already highlighted with crude oil. Traditionally, this benefit can be conceptually compared to owning a call option, where holding the physical commodity provides flexibility to respond to supply disruptions.

However, crypto markets exhibit a different pattern: the convenience yield tends to be negative. Instead of acting like a call option (benefiting from scarcity), holding spot crypto conceptually behaves like owning a put option. This negative convenience yield arises primarily because traders prefer futures contracts for their leverage and speculative potential, leading to an elevated futures price relative to spot (widening futures basis or contango). Additionally, this effect is reinforced by high demand for downside protection, evident in the crypto options markets through increasingly negative volatility skew and elevated put-call ratios. Crypto Out-Of-The-Money (OTM) puts are particularly expensive due to retail traders' demand for crash-risk insurance.

When crypto prices decline, the negative convenience yield amplifies selling pressure: spot holders are incentivized to sell, fueling further price declines and creating a self-perpetuating downward spiral. This sequence was notably observed in 2021, where peaks in futures premiums preceded significant drops in BTC spot prices. Unlike traditional commodities, crypto’s negative convenience yield magnifies volatility and downward price cascades. Owning futures in conventional commodity markets resembles selling a call option, while owning futures in crypto approximates selling a put option. The crypto convenience yield tracks similarly to the “Uniswap Price Doom Loop” in that it is a structurally intrinsic and pervasive short put option within the crypto marketplace.

Crypto can be broadly categorized as an asset class interlaced with steady “Fear-Of-Missing-Out” (FOMO) upside RV and the complementary specter of ominously steep downside IV. Simply put, crypto prices adhere to an “up the stairs, down the elevator” framework. As underlying prices gradually drift upwards under the domain of futures contango, an implied variance asymmetry develops where the perception of future downside risk looms over that of future upside risk. This comparative imbalance in IV continues to bear out when viewing the relative valuation of OTM Panoption put wings over OTM Panoption call wings.

The empirical status quo within the crypto niche is that realized price upticks are ostensibly followed by impending options-implied doom. This notion is solidified even more so when factoring in that directional persistence is sharpened during states of accentuated futures contango or backwardation. RV happens to also be additionally cluster-prone through hiked periods as opposed to suppressed periods, and regarding crypto, hiked RV has clearly proven to reside within the confines of contango. The raised IV preceding periods of backwardation simply acts as a forward-looking counterbalance.

Hearkening back to a question in a previous portion of this study as to how to trade maximized underlying contango or backwardation through options, the answer appears to be to undertake a contrarian view. When contango (backwardation) and upside (downside) realized directional persistence culminate to unusually exhaustive levels, the natural response in the volatility markets is to trade an outlook that portends to be counter to those underlying extremes, probably in the form of OTM option wings. It does bear reiterating though that the recurring theme generally observed within crypto consists of underlying contango and upward persistence attaining new heights, while collaterally on the implied side, downside price convexity exposure is being accumulated through long OTM put wings as perceived preparation for negatively slated future price risk. This realized versus implied pricing rubric is analogous to a quantitative rollercoaster where what actually goes down is sequentially forecasted to go up and vice versa.

In this article, we have unified the conceptual buckets of futures term structure, the VRP, and volatility clustering. This union not only constitutes a distinctive approach to identify when and how longing/shorting synthetic perps on Panoptic would be profitable, but it represents exactly why crypto is a rarefied sub-asset class in terms of RV-IV interplay as well. This type of trading prescription is simple and has potential to be highly lucrative. Lean into crypto underlying extremes from a realized perspective, while trading the opposite from an implied perspective. Such a realized-versus-implied crypto dichotomy presents a myriad of actionable disparities in trading options against underlying delta-one instruments across a full spectrum of centralized and decentralized platforms.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Introduction

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In markets where prices move back and forth without a clear trend, traditional directional trades often perform poorly because of sudden reversals and uncertainty. Panoptic, a DeFi protocol offering perpetual options, takes a different approach: it allows traders to earn from volatility by using non-directional strategies that collect fees over time. One of the most effective tools in this setup is the use of multi-leg strategies, which involve entering multiple option positions—usually a call and a put—at different strike prices. These strategies don’t rely on predicting whether the market will go up or down. Instead, they aim to earn steady income from price staying within a range, while managing risk in a balanced way.

Unlike traditional options, Panoptic’s contracts are perpetual and on-chain, with no expiration date. This introduces an additional layer of flexibility for strategy construction: yield is determined by time-in-range rather than time-to-expiry. Multi-leg strategies in this framework allow traders to define precise risk/reward corridors and collect fees based on option activity rather than one-off premium pricing.

This research byte—Part 4 of the Panoptions Strategies series—focuses on two multi-leg volatility strategies: the short straddle and short strangle. These are implemented on the ETH/USDC 30 bps Uniswap v3 pool using Panoptic’s perpetual options framework. In contrast to Part 3, where we analyzed the long versions of these strategies (which benefit from directional breakouts and expanding volatility), this installment examines the inverse: short volatility positions that thrive when prices remain range-bound and muted.

We compare the performance of short straddles and strangles under various rolling frequencies, assess breach behavior, and quantify fee harvesting efficiency. This transition from long to short volatility gives us a full-spectrum understanding of how to position across different market conditions using Panoptic’s streaming premium model.

Strategy Mechanics

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Straddle

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Short straddles are volatility-selling strategies where traders simultaneously sell a call and a put at the same strike price (typically at-the-money). This results in an inverted "V-shaped" payoff, where profits are maximized if the underlyer stays near the strike and losses occur with large directional moves.

• Profit if the underlying price stays close to the strike.
• Max gain: total streamia collected while both legs remain in-range.
• Risk: unlimited loss if ETH moves sharply up or down.
• Ideal market: low volatility, mean-reverting price action.

This strategy mirrors the perpetual straddle structure by placing a short call and put directly at the spot price, forming a narrow, high-premium range. The short straddle maximizes fee collection when ETH stays near the strike but is more sensitive to directional moves. It thrives in low-volatility, mean-reverting environments — ideal for harvesting theta when price remains tightly contained.

Strangle

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Short strangles reduce cost and risk exposure by selling out-of-the-money puts and calls at different strikes, generating revenue across a wider price band. The trader profits if ETH remains between the two strike prices but can face large losses if the price breaks out in either direction.

• Profit if the underlying stays between the OTM strike levels.
• Max gain: limited to the total streamia collected.
• Risk: significant if ETH trends beyond either leg.
• Ideal market: stagnant or range-bound conditions.

This strategy mirrors the perpetual straddle structure but repositions the short call and put legs further from the spot price, forming a strangle. This wider range can improve profitability by staying in-range longer, albeit with potentially less streamia collected. The short strangle thrives when ETH meanders between the strikes and decays quickly if price stays contained — ideal for harvesting theta without taking a strong directional view.

Note on Delta Neutrality

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Are short straddles and strangles delta-neutral strategies?

Yes — but only initially. Both short straddles and short strangles are delta-neutral at entry, meaning they have no immediate directional bias. A short straddle sells both an at-the-money (ATM) call and put, which offsets deltas symmetrically. Similarly, a short strangle sells out-of-the-money (OTM) options on both sides with matching deltas, resulting in a net delta of 0.

However, as the underlying price moves, the position's delta drifts. If price rises, the short call becomes more sensitive (more negative delta), and if price falls, the short put dominates (more positive delta). Without rolling, the strategy becomes increasingly directional.

In Panoptic, since options are perpetual and not automatically re-anchored, this drift happens continuously. Rolling the position daily or weekly helps maintain practical delta neutrality by re-centering the strategy around the new spot price.

In summary: short straddles and strangles are delta-neutral at entry, but only remain so with active rolling or dynamic hedging.

Figure 1: Payoff comparison between short straddle and short strangle strategies, illustrating how both benefit from prices remaining near the strike(s). The short straddle generates returns as long as the price stays close to the spot, while the short strangle requires the price to remain within a wider range to avoid losses. Both strategies collect fees over time, but are exposed to losses if the price moves significantly beyond the strike boundaries.

Figure 2: Payoff Comparison of Long Strangle vs. Long Straddle on Panoptic — This figure displays the UI payoff curves for two volatility strategies on Panoptic: the Long Strangle (left) and the Long Straddle (right). The Long Strangle combines an out-of-the-money call (strike 3128) and put (strike 2345).

Data

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To evaluate the performance of short straddle and short strangle strategies on ETH/USDC, we simulate monthly option positions using a range factor of 1.27, the equivalent of an LP position that is concentrated 27% above and 27% below the current price. The backtest period spans one year, from May 2024 to April 2025, just like in part 3. For the short straddle, we take simultaneous short positions in both a call and a put option at the current market price, thereby maximizing fee collection near the spot price. For the short strangle, the call and put positions are placed further apart to reflect out-of-the-money exposure, aiming to collect fees across a broader range. These strategies are designed to profit from low volatility and price stability, earning streaming fees as long as ETH remains within the defined range. Although options are undercollateralized on Panoptic, we assume strategies are fully collateralized for these backtests, incur no trading commissions, and are evaluated using historical Uniswap v3 pool data with a 0.3% fee tier on the Ethereum network.

In this backtest, we evaluate daily, weekly and monthly rolling frequencies to measure how often straddle and strangle positions are reset around the market price. daily rolling offers tighter alignment with short-term volatility, while weekly and monthly rolling captures broader directional moves and amplifies longer term payoff dynamics.

Feel free to check out the code here

Important Note:
One key factor not accounted for in this analysis is the spread multiplier , which is likely greater than 1x. In fact, observed data shows an average spread multiplier of approximately 1.2x. This implies that, when the spread multiplier is equal to 1, the option premium reflects its theoretical value with no adjustment. However, when the spread multiplier is greater than 1—in our case, 1.2x—This means the actual trading conditions deviate from the base pricing due to increased option buyer demand. In this case, buyers pay 20% more than the expected price, making options more expensive to purchase. Conversely, sellers benefit from this spread, earning 20% more than the base premium, which makes selling options more profitable under these conditions.

Results & Interpretation

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Figure 3: ETH/USDC price dynamics from May 2024 to April 2025 in the 30 bps Uniswap v3 pool. The market shows both strong price moves and long sideways periods—making it a great environment to test how straddles and strangles perform using Panoptic’s streaming fee model.

Figure 4: Daily, weekly, and monthly percentage changes in ETH price from May 2024 to April 2025. These changes dynamics provide important context for evaluating short straddle and strangle performance, particularly under different rolling frequencies.

Looking at this ETH price chart, spanning from May 2024 to April 2025, we can identify several distinct phases that are ideal for evaluating short straddles and strangles. ETH began near three thousand dollars, rallied to over four thousand by late 2024, and then sharply declined to around eighteen hundred in early 2025 — a dramatic 56% drawdown from the peak.

What’s particularly interesting is how the price action unfolds: we see a prolonged choppy, sideways period throughout much of 2024, where ETH remained tightly range-bound. These low-volatility conditions are ideal for short straddles and strangles, as the price staying within the option range allows sellers to accumulate streaming fees without significant exposure to directional risk.

However, the sharp drop at the beginning of 2025 presents a stark contrast. These types of sudden directional moves are exactly the kind of events that can challenge short volatility strategies, especially strangles, where wider wings may still get breached. That said, with tight rolling frequency (e.g., daily), short sellers may have managed risk effectively by frequently re-centering their exposure. But clearly, this drawdown period underscores the importance of active management and dynamic strike placement when running short gamma strategies in Panoptic.

In the backtest results, cumulative performance of ETH short straddle and strangle strategies across daily, weekly, and monthly rolling intervals. Each subplot highlights how premia collection, directional payoff, and net return vary under different volatility regimes and strategy designs. To evaluate the risk-return characteristics of short volatility strategies on ETH, we compare short straddles (monthly 50 delta options) and short strangles (monthly 30 delta options) across three rolling intervals: daily, weekly, and monthly. The charts decompose returns into premia (fees earned while the option remains out-of-the-money), payoff (realized token movement due to price breaches), and the net return, allowing for detailed insight into how these strategies perform under different market regimes.

Figure 5: Daily-rolling returns for ETH short strangle (30 delta) and short straddle (50 delta) strategies from May 2024 to April 2025.

Figure 6: Weekly-rolling returns for ETH short strangle (30 delta) and short straddle (50 delta) strategies from May 2024 to April 2025.

Figure 7: Monthly-rolling returns for ETH short strangle (30 delta) and short straddle (50 delta) strategies from May 2024 to April 2025.

Table 1: Summary statistics and Sharpe ratios for short straddle and short strangle strategies across rolling intervals

Starting with the daily rolling interval, both straddle and strangle strategies exhibit relatively low volatility and tight clustering around zero. Occasional drawdowns do appear, especially in response to abrupt price movements like those in March 2025. However, the short straddle clearly benefits more from the daily re-centering effect. It consistently collects higher premia due to its at-the-money (ATM) positioning and exhibits greater return stability across the year. In contrast, the short strangle, while more resilient to minor intraday fluctuations due to its wider range, captures less premium and shows slightly more vulnerability during fast directional moves.

The weekly rolling plots offer a balanced perspective. Both strategies achieve more stable return profiles compared to the monthly charts while allowing for more capital efficiency than daily rolling. Weekly straddles produce consistent fee accumulation and moderate drawdowns, typically not exceeding -6%. The weekly strangle also improves in stability compared to the monthly version, but still underperforms the straddle overall. The shorter rolling horizon ensures quicker strike re-centering after large moves, which helps contain loss severity and allows return recovery in the following weeks.

In the monthly rolling plots, the differences become more pronounced. Both strategies are exposed to more prolonged directional risk, but the short strangle demonstrates significantly deeper losses. For instance, in months like August 2024 and March 2025, the short strangle reaches drawdowns as steep as -14%, while the short straddle tends to limit its worst-case returns to the -11% range. Despite this, both strategies show strong positive returns during calm months like October 2024, February 2025, and April 2025, with the short straddle again outperforming due to its richer fee collection. The monthly strangle, while capable of producing good returns in sideways markets, suffers heavily when ETH breaks out directionally, reflecting the high gamma exposure over extended windows.

Quantitatively, the short straddle dominates in terms of sharpe ratio and return consistency. Its tighter strike placement yields greater premia, and the frequent OTM condition ensures fee income builds up reliably. The strangle only outperforms in long, low-volatility phases where the spot price drifts but stays well within its OTM range. However, when breached, its wider wings deliver harsher payoffs and slower recovery. This makes the strangle strategy particularly vulnerable under high-volatility breakouts.

Rolling frequency is a critical determinant of performance. Daily rolling minimizes directional exposure and quickly re-centers positions, making it ideal for volatile environments. Weekly rolling strikes a balance between fee harvesting and directional risk. Monthly rolling is capital-efficient but risky unless volatility remains low for extended periods.

Win Rate Analysis Across Frequencies

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To further quantify the reliability of short straddle and short strangle strategies, we evaluate their empirical win rate — defined as the percentage of periods with strictly positive net returns. This metric offers a complementary perspective to the Sharpe ratio, highlighting the consistency of profitable outcomes rather than their magnitude or volatility-adjusted efficiency.

Table 2: Win rates across rolling intervals for short straddles and short strangles.

As shown in Table, both strategies exhibit moderate-to-high win rates across all rolling intervals. Daily rolling displays the strongest consistency, with short straddles achieving a 70.96% win rate and short strangles closely following at 68.22%. Weekly frequencies also perform reliably, with win rates clustering near 58.49% for short straddle and 60.38% for short strangles. Monthly rebalancing, while more volatile in terms of payoff magnitude, still achieves a 66.67% win rate for both strategies, indicating that even with fewer rolling opportunities, premium collection and range containment often yield net-positive outcomes.

Conclusion & Future Work

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In conclusion, short straddles exhibit peak gamma exposure precisely when the underlying hovers near the strike, meaning even small price movements around that level can trigger disproportionately large changes in directional risk. In Panoptic, the risk associated with these strategies is distinctly nonlinear—losses are not solely triggered by a breach of the LP range but grow the deeper the price pushes into either leg. Both the magnitude and the speed of price movement matter: a slow drift beyond the strike may still result in manageable losses, while a sharp spike can rapidly unwind multiple cycles of accrued fees.

Additionally, since Panoptions stream yield only while one or more legs remains in range, the timing of price movement is critical. If ETH breaches a leg early in the cycle, that leg ceases to collect fees, dramatically reducing net returns. Consequently, two price paths ending near the same level can yield vastly different outcomes based on how long each leg remained inactive. Furthermore, while short straddles and strangles may be delta-neutral at entry, they are not risk-neutral. Convexity—i.e., gamma risk—grows the longer the strategy is left unadjusted.

On the other hand, more frequent rolling helps maintain neutrality but increases exposure to re-entry at potentially less favorable volatility levels. Ultimately, these strategies display a characteristically skewed return profile: many small, steady wins punctuated by rare but severe losses. With win rates commonly exceeding 60%, a single volatile move (i.e. a sudden $1,000 drop in ETH) can wipe out months of gains, underscoring the importance of position sizing and risk limits in DeFi-native volatility harvesting.

This study opens several promising avenues for future research. First, applying the short straddle and strangle framework to other Uniswap v3 pools—such as WBTC/USDC or ETH/stETH would help evaluate strategy robustness across different volatility profiles and liquidity conditions. Second, deeper delta optimization could be achieved by conditioning strike selection on historical breach frequency or volatility clustering, enabling more responsive positioning. Third, incorporating risk-adjusted metrics like Sharpe and Sortino ratios would offer a clearer view of return consistency and tail risk across rolling intervals. Finally, exploring alternative rebalancing triggers such as volatility spikes, breach proximity, or fee decay thresholds may significantly improve risk management and capital efficiency compared to fixed calendar-based rebalancing.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Feel free to check out our livestream video on YouTube!

One of the more relatively underexplored elements of volatility trading is the volatility of implied volatility (IV) or “vol-of-vol.” This empirical property is tradable through the options Greek of volga, which expresses changes in vega with respect to changes in IV ($\frac{\partial \nu}{\partial \sigma}$). The logical question for our purposes then becomes how does volga present itself in Panoptions trading?

A key parallel to comprehend is that volga is shorthand for “volatility gamma,” meaning that explicitly trading in this higher-order Greek bears a mechanical resemblance to either gamma scalping or reverse gamma scalping depending on whether a long or short volga position is undertaken. However, a core distinction to understand is that where gamma trading relates to convexity or payoff curvature concerning underlying spot price, volga trading is predicated on convexity with regard to volatility or vega. Purchasing or selling volga is fundamentally akin to respectively longing or shorting the convexity of volatility.

Liquidity provider (LP) shares on Uniswap have already thoroughly proven to contain negative gamma or negative price convexity as they essentially function as short perpetual put option positions. This embedded asymmetry leads to the “Uniswap Price Doom Loop” where the underlying must be sold amid price downturns to maintain delta-neutrality. What if this structurally biased dynamic also extends over to vega convexity for Uniswap-based perpetual options? And, if so, how could such a trait be profitably navigated and traded?

Results

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In the context of this study, volga exposure is maximized and traded through running backtests on Panoption reverse iron butterflies for the ETH/USDC and WBTC/USDC 30bps Uniswap pools. The reverse iron butterfly strategy consists of a long At-The-Money (ATM) straddle and short Out-of-the-Money (OTM) strangle. Deep OTM options contain peak volga, while volga bottoms for ATM options. ATM options are limited to only linear exposure with respect to volatility with deep OTM options (wings) possessing convexity with respect to volatility. Options wings majorly benefit from magnified vol-of-vol due to the enhanced probability of migrating from deep OTM to In-the-Money (ITM).

The call and put option legs featured in our backtested strangle were selected to be struck at the 10-delta level as volga crests at this moneyness tier (displayed per the graphic above). Given the potential predisposition to short vega convexity environments for Panoptions that was previously outlined, we specifically selected the reverse iron butterfly to backtest as it is intrinsically a short volga strategy. As the above table aids in delineating, the conventional iron butterfly (long OTM strangle, short ATM straddle) naturally stands in contrast as a long volga strategy.

The above charts reveal the reverse iron butterfly monthly results on the ETH/USDC 30bps pool ranging from May 2021 through May 2025 (see code here). The cumulative return through this period sums to 59% (12% annualized). This short volga strategy supplies a steady year-over-year yield over an array of market climates throughout this 4-year sample. On a monthly basis, the strategy performs well whenever there is extreme volatility skew of either directionality, but this effect is specifically more pronounced in the presence of accentuated positive skew. This observation aligns with the “relief risk premium” property where vol-of-vol is significantly reduced in the wake of market uncertainty resolution.

As shown above, the WBTC/USDC pool reverse iron butterfly monthly returns are muted by comparison when backtested during an identical sample period as the ETH/USDC pool. The returns for the 4-year span accumulate to a total of 17%, which translates to a mere 3.9% return when annualized. Month-over-month, the same general trend observed with ETH also applies to BTC where strategy performance is enhanced by volatility skew extremities of either direction. Though the highest monthly strategy returns for BTC, much in the same vein as ETH, are spurred on by abnormally positive volatility skew.

Although, both ETH and BTC are rarities when viewed against other asset classes in the sense that they generate positive returns at all when deploying a long-term, short vol-of-vol strategy. Why is this the case with ETH and BTC being short volga standouts? We look to further statistical analysis.

Broader Discussion & Conclusions

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Spanning from May 2021 through May 2025, the above graphics showcase the rolling 30-day standard deviations of daily changes in the Uniswap IV for the ETH/USDC and WBTC/USDC pools as well as the rolling 30-day correlation between daily changes in Uniswap IVs and their respective rolling standard deviations during that time. While ETH and BTC each exhibit individual trends in terms of vol-of-vol, the correlation of IV to vol-of-vol of both assets occupy positive territory for a fairly sizable duration of the sample. The full sample correlations are 0.51 and 0.35, respectively, for ETH and BTC with ETH deviating more than BTC around the mean of 0. ETH also has a marginally higher vol-of-vol for the sample than BTC. These are all contributing factors to ETH being assessed with an elevated vol-of-vol risk premium.

The vol-of-vol risk premium is a premium stemming from the heightened perception of possible vol-of-vol risk for the underlying asset. So as with any risk premia, there is an opportunity to “fade” or bet on the eventual mean-reversion of the premia to a more normalized level. The short volga trade resultantly becomes more attractive for ETH and BTC predominantly due to increased IV/vol-of-vol correlations. For the sake of comparison, the VIX/VVIX correlation is observed to be 0.27, lower than both ETH and BTC. A long volga strategy is generally more conducive for equities as demonstrated by the below chart.

The “BWB” metric on the above visualization is indicative of excess returns for a portfolio of S&P 500 equities where the underlying equities with the highest iron butterfly returns are systematically bought, and accordingly, the equities with the lowest iron butterfly returns are systematically sold over the course of a 24-year timeline. This portfolio management technique consistently outperforms the baseline S&P 500 market benchmark (“MKTRF”) for a healthy portion of the sample in question.

When accounting for a subdued IV/vol-of-vol correlation, a long volga strategy such as a conventional iron butterfly is hence proven capable of reaping in considerable alpha within equities because the asset class-specific vol-of-vol risk premium is not deemed to be as steep. The opportunity for a mean-reversion trade is expanded in tandem with a temporarily inflated perception of risk, so it stands to reason that as an IV/vol-of-vol correlation is abnormally hiked, there is a greater likelihood for vol-of-vol risk to be mispriced in the interim. Such a mispricing becomes apparent when analyzing how reverse iron butterfly returns align in perfect descending order with the associated IV/vol-of-vol correlation for ETH, BTC, and S&P equities.

The shared intuition between hedging gamma and volga has already been illustrated in this analysis, but the potential reverberations from negative vega convexity hedging on Panoptic have yet to be fully realized. Just as the process underpinning reverse gamma scalping entails buying the underlying into rallies and selling the underlying into downturns to delta-hedge, short volga trading involves buying options as IV rises and selling options as IV declines for the objective of vega-hedging. This joint trading intuition also bears out mathematically through the following equations in that:

Reverse Gamma Scalping P&L:

(1)

& Short Vol-of-Vol P&L:

(2)

Both tactics hinge on implied parameters surpassing their realized counterparts over an elapsed period of time with volatility being the relevant component for reverse gamma scalping and vol-of-vol pertaining to short volga trading. Whereas underlying price reflexivity is a byproduct of reverse gamma scalping when peak prices are pushed higher and troughed prices are pushed lower to hedge, an apex IV would be forced higher and a depressed IV would be forced lower due to the machinations of short volga trading.

Does a viable short vega convexity climate for Panoptions lay a solid foundation for a uniquely reflexive volatility feedback loop on the platform? Or does a similarly outsized vol-of-vol risk premium occur in offchain crypto options trading as well? Reconciling these answers could possibly amount to a panoply of arbitrage opportunities.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Feel free to check out our livestream video on YouTube!

Introduction

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In volatile, range-bound markets, traditional directional strategies often underperform due to frequent price reversals and uncertain trend conviction. For DeFi-native option protocols like Panoptic, this presents a unique opportunity: to harvest volatility through streaming fees by deploying non-directional, high-theta strategies such as multi-leg strategies. By multi-leg, we generally mean that we are involving simultaneously buying and selling multiple options contracts with different strikes, expirations, or both. They're designed to profit from specific market conditions while managing risk and capital efficiency. Here in our case there’s no expiration date since the options in Panoptic are perpetual which makes things even more interesting, profit-wise. Multi-leg options strategies offer primary advantages that make them attractive to sophisticated traders especially from a risk management perspective, they provide limited maximum loss exposure with clearly defined profit zones and breakeven points while requiring less capital than single option positions.

This research byte investigates two multi-leg strategies: straddles and strangles. These strategies are implemented on the ETH/USDC 30 bps Uniswap v3 pool using Panoptic’s option framework. This is a part three of our Panoptions strategies research series, where we systematically backtest both long and short positions on calls and puts. In this installment, we extend the analysis to multi-leg volatility strategies—specifically straddles and strangles—and examine their performance under different rolling intervals using Panoptic’s streaming premium model.

Strategy Mechanics

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Straddle

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Straddles are volatility-focused options strategies that involve buying both a call and put option at the same strike price (typically at-the-money). This creates a symmetric "V-shaped" payoff profile where the strategy profits when the underlier moves significantly in either direction

• Profit if the underlying price moves significantly in either direction.
• Max gain: unlimited upside if the underlier rises, or large gain if ETH falls sharply.
• Risk: limited to the total streamia paid for both legs.
• Ideal market: highly volatile with large, unpredictable moves.

Strangle

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Strangles, on the other hand, offer a more cost-effective approach to volatility trading by purchasing out-of-the-money call and put options at different strike prices, creating a wider "profit dead zone" between the strikes. This strategy requires larger price movements to become profitable since the underlier must break beyond either OTM range, but compensates with lower costs compared to straddles.

• Profit if the underlying price moves beyond either OTM strike level.
• Max gain: unlimited if the underlier trends strongly up or down.
• Risk: limited to the total streamia paid, typically lower than for a straddle.
• Ideal market: directional breakout after low volatility.

This strategy mirrors the perpetual straddle in structure but modifies the placement of the legs to simulate a strangle. Instead of centering both legs at the current price, the long call and long put are positioned further out-of-the-money. This potentially lowers costs, but requires larger price moves for the strategy to become profitable. The strategy still relies on streaming fee accumulation once price reaches either leg’s defined zone. The strangle benefits more from strong directional breakouts and minimizes premium drag during sideways markets.

Notes: Straddles and strangles are both delta-neutral at initiation — they don’t care which direction the market moves, only that it moves, making them perfect for traders who lack directional conviction but expect volatility. Furthermore, straddles are placed right at the current price (ATM), so they react quickly to even small moves, but that precision comes with a higher premium. A compelling aspect is that before major events like Fed meetings, earnings announcements, or crypto upgrades, straddle prices often spike, since they’re a direct bet on expected volatility. As a final point, strangles let you choose how far out-of-the-money to place each leg, giving you control over the width of your profit zone — deeper OTM strikes cost less, but require larger price moves to pay off, making them ideal for betting on big swings at a lower cost.

In Panoptic, options are perpetual, and premiums accrue as streaming fees over time when liquidity is in-range. For straddle and strangle sellers, this transforms theta from a decaying liability into a positive revenue stream. These straddle strategies are designed to maximize time-in-range for both call and put legs. On the other hand, it is important to note that by frequently rolling both legs around the ATM price, each strategy harvests volatility, not through price direction, but through mean reversion and touch frequency. In effect, these are theta-maximizing, delta-neutral positions for DeFi-native traders.

Figure 1 Payoff comparison between long straddle and long strangle strategies, illustrating how both benefit from large price movements in either direction, with the straddle activating closer to the spot and the strangle requiring a wider move to generate returns.

Figure 2 Payoff Comparison of Long Strangle vs. Long Straddle on Panoptic — This figure displays the UI payoff curves for two volatility strategies on Panoptic: the Long Strangle (left) and the Long Straddle (right). The Long Strangle combines an out-of-the-money call (strike 3128) and put (strike 2345).

Data

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To evaluate the performance of straddle and strangle strategies on ETH/USDC, we simulate monthly option positions with a range factor of 1.27. The backtest period is one year, from May 2024 to April 2025. For the straddle, we construct a symmetric exposure by simultaneously entering both a call and a put option at the current market price. For the strangle, we place the call and put further apart from the current price to reflect OTM exposure on both sides. These positions are designed to capture profits from price volatility without taking a directional view. For the purpose of this backtest, all strategies are fully collateralized, incur no trading commission, and are evaluated using historical Uniswap v3 pool data with a 0.3% fee tier on the Ethereum network.

In this backtest, we evaluate both weekly and monthly rolling frequencies to measure how often straddle and strangle positions are reset around the market price. Weekly rolling offers tighter alignment with short-term volatility, while monthly rolling captures broader directional moves and amplifies long-term payoff dynamics.

Feel free to check out the code here

Important Note:
One key factor not accounted for in this analysis is the spread multiplier, which is likely greater than 1x. In fact, observed data shows an average spread multiplier of approximately 1.2x. This implies that, when the spread multiplier is equal to 1, the option premium reflects its theoretical value with no adjustment. However, when the spread multiplier is greater than 1—in our case, 1.2x—This means the actual trading conditions deviate from the base pricing due to increased option buyer demand. In this case, buyers pay 20% more than the expected price, making options more expensive to purchase. Conversely, sellers benefit from this spread, earning 20% more than the base premium, which makes selling options more profitable under these conditions.

Results & Interpretation

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Figure 3 ETH/USDC price dynamics from May 2024 to April 2025 in the 30 bps Uniswap v3 pool. The market shows both strong price moves and long sideways periods—making it a great environment to test how straddles and strangles perform using Panoptic’s streaming fee model.

Looking at this ETH price chart spanning from May 2024 to April 2025, we can see some really interesting patterns that are perfect for our options backtesting. ETH started around three thousand dollars, rallied to over four thousand in late 2024, but then got hit hard and dropped all the way down to about eighteen hundred dollars - that's a massive 56% decline from the peak. What's fascinating here is how the price moves in these distinct phases. You can see we had this sideways, choppy period through most of 2024 where ETH was just grinding. Then boom - we get this explosive decrease in the beginning of 2025.

This kind of price action is exactly what we want when testing straddles and strangles. During those choppy, low-volatility periods, straddles would have been collecting premium nicely as the price stayed range-bound. But then during these big breakout moves especially that massive drop we're seeing now that's where strangles really shine, particularly if you had those out-of-the-money puts positioned correctly.

Figure 4 Cumulative performance of ETH long straddle and strangle strategies across weekly and monthly rolling intervals. The charts break down total returns into fee income (premia), directional gains (payoff), and net results, illustrating how volatility regimes and rolling frequency influence the trade-off between premium decay and realized PnL.

The comparative performance of long straddle and long strangle strategies on ETH/USDC, as illustrated in the figures, highlights how structure and cost sensitivity shape their outcomes under Panoptic’s perpetual option framework. All short strategies show strong premium collection - short straddles earning 45-52% and short strangles 43-51% demonstrating the power of selling volatility in crypto markets. Moreover, monthly rebalancing consistently outperforms weekly by twice as much for both long straddles and long strangles, showing that less frequent adjustments on long positions capture price swings more effectively.

The long straddle, which places both the call and put at the at-the-money strike, responds more quickly to short-term price fluctuations. However, this sensitivity comes at a cost. Because both legs are active around the spot price, premium accrues continuously, even in low-volatility environments where neither leg generates meaningful payoff. This results in a performance profile where cumulative payoffs trend upward but are largely offset by the persistent drag of streaming fees. What's even more fascinating is that even though straddles have an immediate activation of the legs, strangle still outperformed the straddles at the end of the one year backtest: 3.28% for straddles against 10.46% for strangles. In fact, the long strangle—constructed with out-of-the-money legs—shows a more favorable risk/reward profile. Since each leg activates only when ETH moves beyond a wider threshold, premium decay is lower and more episodic. This design allows the strangle to perform well during breakout phases while remaining relatively insulated during quiet periods.

Figure 5 Performance breakdown of ETH long straddle (50 delta) and strangle (30 delta) strategies across weekly and monthly rolling intervals, highlighting differences in fee accumulation, directional payoff, and overall return dynamics under varying volatility conditions.

When examining the granular return charts, we observe that generally speaking, there isn't much difference in the performances of these two strategies in terms of the patterns of the returns. However, straddles seem to have the highest monthly return in both rolling frequencies, while, strangles still outperformed the straddles at the end of the backtest.

Ultimately, straddle and strangles returns are higher with monthly rolling because the longer holding period allows each leg to stay active and capture larger price moves, increasing the chance of significant directional payoff. In contrast, weekly rolling resets more frequently, keeping the position close to spot but often missing extended trends. Since these strategies always sit near the current price, they continuously incur streaming fees in Panoptic. Monthly rolling gives the strategy more time to overcome this fee drag, while weekly rolling effectively caps upside potential.

Conclusion

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At the end of the chaotic one-year backtest, the long strangle outperforms in breakout-driven markets due to its lower cost and wider profit range. Nevertheless, it lags during low-volatility periods when price stays between its strikes. The long straddle, while more sensitive to small price moves near the entry point, suffers from higher fee accumulation over time. However, the data shows straddles can make you between 10% and 15% monthly when there's a conviction of volatility. Furthermore, rolling frequency does matter at the end of the day: monthly rebalancing captures larger directional moves more effectively.

On the other hand, a natural next step is to extend this analysis to short straddle and short strangle strategies, which invert the payoff profile and introduce asymmetric risk in exchange for steady premium accumulation. Studying these positions would allow us to quantify theta harvesting opportunities and stress-test capital efficiency under tail events.

Another promising direction is to dynamically adjust the delta and width of each leg based on realized or implied volatility regimes. For example, tightening strikes in low-volatility environments or widening them ahead of anticipated macro events could enhance performance through volatility targeting.

It would also be valuable to explore multi-leg combinations, such as iron condors or butterfly spreads, which may offer more favorable risk-adjusted returns in range-bound markets with lower directional bias.

Moreover, to make the simulation more realistic, future work could use actual historical tick data to measure how long price stays in each range and estimate fee accrual more accurately. The analysis could also be expanded to include other assets and different fee tiers, like 5 bps pools, to better understand how Panoptic strategies perform across various market conditions.

In the end, whether you choose straddles or strangles, you're essentially making the same bet: that ETH will move big, move fast, and move in your favor. Just remember - in the world of long volatility strategies, you're not just trading options, you're trading on chaos itself. And in crypto, chaos always delivers...eventually!

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Feel free to check out our livestream video on YouTube!

One of the more prevalent and pervasive higher-order options Greeks is encapsulated by vanna, which can be interpreted in two different ways: (1) changes in delta with respect to changes in implied volatility (IV) ($\frac{\partial \Delta}{\partial \sigma}$) or (2) changes in vega with respect to changes in the underlying spot price ($\frac{\partial \nu}{\partial S}$). Vanna fundamentally quantifies the exposure of an options portfolio to spot-implied volatility (or spot-vol) correlation.

Now that the conceptual foundation for spot-vol correlation has been established, it is also worth asking:

How do asymmetries in spot-vol correlation manifest themselves in various asset classes?

Equity indexes are known to exhibit a strongly negative spot-vol correlation, meaning that as IV rises, equity prices conventionally decline. Whereas in certain commodities such as gold, the opposite process transpires in that prices elevate alongside IV, otherwise known as positive spot-vol correlation. Meanwhile, crypto spot-vol correlation has displayed a tendency to oscillate between both positive and negative territory.

In this article, we will dive into patterns that define onchain crypto spot-vol correlation as well as how to capitalize on these patterns through Panoptions.

Results

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We elected to trade on our view of underlying spot-vol correlation and maximize respective vanna exposures by conducting backtests for 15-delta Panoption risk reversals on the ETH/USDC and WBTC/USDC 30bps Uniswap pools. A positive (negative) risk reversal is an options strategy consisting of buying (selling) an OTM call option, while simultaneously selling (buying) an OTM put option. The 15-delta level was selected as the optimal moneyness for the risk reversal backtests as vanna is maximized at that delta threshold (as shown per the figure below).

15-delta calls are assigned positive vanna with 15-delta puts being assigned negative vanna, so 15-delta positive risk reversals will theoretically benefit from extremes in positive spot-vol correlation, while 15-delta negative risk reversals will reap the rewards of extremes in negative spot-vol correlation. Per standard prescription of volatility skew, the intuitive reasoning behind these vanna designations being that the IV for call options rises as the underlying price rises, but the IV for put options conversely rises as the underlying price decreases.

We have also chosen to showcase the months with the highest risk reversal returns over a 4-year sample ranging from May 2021 to May 2025. Although risk reversals are capable of generating steady yields through many market climates, the primary purpose of this study is to emphasize how certain indicators can be used to empirically pinpoint inflection points in directional trends. Specifically, we will hone in on rolling spot-vol correlations and underlying return persistence as tools to aid in detecting ripe environments for maximally deploying either long or short vanna positions.

This regime-dependent approach will allow us to explore the deeper nuances of these indicators to optimize the timing and structure of risk reversals for comparison across abbreviated, pressurized periods defined by particular market attributes. The situational nature of profit maximization for risk reversals is very much in line with the conditional criteria and ephemeral base necessary for fruitful gamma scalping.

Spanning from May 2021 through May 2025, the above graphics reveal that the most profitable period for the ETH/USDC 30bps pool positive (negative) risk reversal on an intra-month basis during that sample was July 2022 (May 2022) with a 36% return (17% return). Those monthly returns amount to annualized totals of 3,910% and 559%, respectively, for the 15-delta positive and negative Panoption risk reversals (see code here). The ETH/USDC 30bps pool comparatively proves to be more conducive for positive vanna exposure (long vanna) over an abbreviated period rather than negative vanna exposure (short vanna). Although there is a prevailing bias towards positive spot-vol correlation, the combined monthly return of 53% stemming from both risk reversals reveals that Panoptions on the ETH/USDC 30bps pool are prone to spot-vol correlation sensitivity of either positive or negative directionality.

The above illustrations unveil the results for 15-delta Panoption risk reversals on the WBTC/USDC pool with selected monthly returns from the same overall sample as the ETH/USDC pool. The positive (negative) risk reversal yielded a return of 17% (25%) during October 2021 (May 2021), those figures, respectively, translating to annualized returns of 559% and 1,357%. In addition to the Panoption risk reversals on BTC being cumulatively less profitable than those on ETH over the course of a one-month snapshot, the BTC risk reversals also diverge from ETH in that being short vanna is more lucrative than being long vanna. BTC risk reversals thus produce a combined return of 42% with a heightened sensitivity to negative spot-vol correlation over positive spot-vol correlation.

Broader Discussion & Conclusions

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The charts below display the 30-day rolling spot-vol correlation from May 2021 throughout May 2025 for both the ETH/USDC and WBTC/USDC Uniswap pools alongside the 30-day rolling Hurst exponent for both pools during the same sample. The Hurst exponent is a metric designed to quantify the degree of autocorrelation or trendiness within a time series.

A Hurst exponent on asset returns greater than 0.5 is indicative of a favorable trading environment for momentum with a value less than 0.5 signaling a favorable climate for mean-reversion, while asset returns that generate a value around 0.5 are deemed to be governed by a “random walk” stochastic process. In conjunction with the Hurst exponent in our analysis being applied to simple spot returns, the spot-vol correlation results are derived by measuring the rolling correlation between simple spot returns and Uniswap IV.

Based on the above displays, there are two distinct parallels shared by ETH and BTC throughout the sample. One is that not only the absolute level, but the relative “acceleration” of spot-vol correlation–either upward or downward over a given time period–is relevant to risk reversal returns. The other is that steep increases in the Hurst exponent coincide with steep increases in spot-vol correlation, while sudden drops in the Hurst exponent align with sudden drops in spot-vol correlation. Trendier returns thereby serve as a factor in augmenting spot-vol correlation, and mean-reverting returns play a role in diminishing spot-vol correlation.

These results extend the conclusions of prior literature which found that persistent autocorrelation (or trend) is empirically associated with equity bull markets and autocorrelation anti-persistence (or mean-reversion) presents itself during equity bear markets, as the above graph helps to illustrate with the S&P 500 index.

Separate research also corroborates these findings as increasing underlying return autocorrelation is discovered to be a statistically significant and positive predictor of At-The-Money (ATM) equity call option returns over put option returns. The comparable superiority of call option returns in the presence of magnified autocorrelation is visualized below with put option and straddle returns also benchmarked. It bears noting that the returns and statistical significance for these respective options positions is only enhanced when the supplement of delta-hedging is added to the portfolio.

The common theme between our spot-volatility correlation and Hurst exponent findings is that the rate of change relative to both metrics merits further scrutiny and examination. Magnitude and speed of upward or downward fluctuations in spot-vol correlation or the Hurst exponent act as integral complements to the absolute level of either measurement, particularly in periods when the two do speedily fluctuate in concert with each other.

This joint property becomes apparent while specifically observing the timing of when the positive and negative risk reversal returns for ETH and BTC were maximized. Neither ETH nor BTC achieved maximum risk reversal returns during months when the spot-vol correlation or Hurst exponent were at absolute sample peaks or troughs, but all four risk reversals produced outsized gains in tandem with rapid shifts in the two quantities occurring as well as local peaks or troughs in each measure being reached.

This analysis then expands into the rationale of asking: what is the upward/downward “acceleration” threshold for spot-vol correlation and the Hurst exponent to portend higher returns for directional options positions such as the risk reversal? How could such a threshold be derived? And does the rate of change for one of these metrics (spot-vol correlation and Hurst exponent) quantitatively presage the other one? We leave these questions to future research.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Feel free to check out our livestream video on YouTube!

Introduction

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Options strategies offer traders structured ways to express bullish or bearish views with tailored risk exposures. Panoptic enables these expressions in a novel DeFi-native way, transforming Uniswap V3 liquidity positions into perpetual options. Panoptic options are perpetual: as long as the position remains in range (within the Uniswap tick boundaries), streamia flows continuously. Option buyers pay streamia, while sellers collect it. When the price moves out of range, streamia stops, introducing a novel time-premium decay mechanism in DeFi.

This research byte is part two of our Panoptions strategies series, and it examines two bullish strategies using Panoptic on the WETH/USDC 30 Bps pool: short puts and long calls. Both benefit from rising ETH prices, yet they differ significantly in risk exposure, capital efficiency, and premium dynamics. Using historical pool data, we analyze payoff mechanics, yield behavior, and performance trends.

This research article presents a quantitative comparison of short call and long put strategies on Panoptic’s WETH/USDC 30bps pool, using historical data from Jan 2024 to Feb 2025. Both express bearish market views, but with markedly different risk-reward profiles.

The long put strategy with monthly rolling delivered the strongest performance, achieving +20% total returns during major ETH drawdowns (notably in March, August, and February), with limited losses capped at the premium paid.

In contrast, the short call strategy, while consistently earning 2–4% per month in quiet markets, experienced drawdowns of up to -40% during sharp ETH rallies, exposing its vulnerability to tail risk.

Weekly rolling helped reduce loss severity for short calls and enhanced responsiveness for long puts, but did not alter core payoff structures. Ultimately, long puts proved effective as downside protection with defined risk, while short calls offered steady income at the cost of rare but severe losses—underscoring the importance of strategy selection and risk management in DeFi-native options frameworks like Panoptic.

Short Put

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A short put in Panoptic functions like writing a traditional put: the trader earns yield for providing downside insurance.

• Profit when ETH appreciates; losses occur if ETH price declines
• Max gain: streamia collected while the option stays in the range
• Risk: exposure becomes critical during extreme market downturns, with losses escalating as ETH approaches zero
• Ideal market: neutral to bullish

Long Call

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A long call in Panoptic gives the buyer the right to benefit from upward ETH movement.

• Profit if ETH price increases
• Max gain: theoretically unlimited as ETH rises
• Risk: downside is capped at the total streamia paid, offering a clearly defined loss
• Ideal market: strongly bullish

Data & Implementation

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We simulate both strategies using the WETH/USDC 30 bps Uniswap pool from January 2024 to February 2025. We employ rolling (rebalancing) to update positions as the price evolves.

• Use 30-delta puts and calls — in other words, we use out-of-the-money options.
• Monthly options are approximated via a range factor of 1.25, which roughly translates to a one-month option.
• Rolling is applied at two frequencies: weekly and monthly.
• The same DTE (days to expiry) formula from part 1 applies, mapping Panoptic width to implied option expiry. [Insert link]
• We compute accumulated payoffs, premia, and net returns for each strategy and rolling frequency:
  • Payoff is the profit or loss profile of an option as the spot price moves, shaped by the liquidity position’s range and type (e.g., short call, short put).
  • Returns represent the net profit or loss from an options strategy, calculated as the sum of payoff and earned fees, minus commissions (zero in our case), plus any additional yield from providing liquidity. This reflects the total performance of a position over time, accounting for both market movement and protocol-level earnings.

You can view the code here.

You can view the code here

Results

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Figure 1 The WETH/USDC spot price is sourced from the Uniswap V3 30 bps pool, covering the period from January 2024 to February 2025. This timeframe exhibits significant volatility, characterized by a wide range of dynamic price patterns.

Figure 2 Weekly and monthly decomposition of ETH monthly long call and short put returns, premia, and payoff for weekly and monthly rolled options.

Figure 3 Weekly and monthly decomposition of ETH monthly long call and short put returns, premia, and payoff for weekly and monthly rolled options.

Analysis of The Results

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Long Call Strategy Analysis

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Monthly Rolling:
The long call strategy demonstrates strong positive performance during sustained bullish trends, with cumulative returns reaching +24.30% by February 2025. The strategy shows a clear pattern where payoff (green line) is the primary driver of returns during strong upward ETH price movements. While the strategy consistently pays premiums (blue line trending downward to -50.25%), these costs are more than offset by significant payoff gains during bullish periods. The monthly bars reveal several standout months with returns exceeding 15%, particularly in February 2025. This highlights the strategy's leveraged nature - while premium costs are consistent, payoffs can be substantial when the market moves favorably. The strategy demonstrates its effectiveness as a directional bet on ETH price appreciation, particularly during the strong uptrend from late 2024 into early 2025.

Weekly Rolling:
With more frequent position adjustments, the long call strategy achieves even stronger performance, with cumulative returns reaching +8% to +10% in July 2024, August 2024, and the beginning of 2025, and still ends with positive returns of around 5%.
Weekly rolling allows the strategy to better capture intermediate price movements and adjust positions more dynamically as market trends develop, even though it seems that monthly returns are more interesting for generating more net returns—24% against 5%. On the other hand, premium costs are higher (blue line reaching -60.27%) due to more frequent trading, but payoff potential is reduced (green line reaching above 65%). The weekly component bars show numerous small positive return instances punctuated by several larger spikes exceeding 10%, demonstrating how the strategy can capitalize on shorter-term price movements. Notably, the cumulative return line shows more consistent upward momentum compared to the monthly rolling version, suggesting that more frequent adjustments help the strategy maintain alignment with the market direction throughout the trading period.

Short Put Strategy Analysis

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Monthly Rolling:
The short put strategy demonstrates consistent premium income (blue line trending upward to +39.89% cumulatively), highlighting its primary function as an income-generating strategy. However, this comes at the cost of occasional significant drawdowns in the payoff component (green line), which represents the inherent risk of selling downside protection. The overall return (pink line) shows modest negative performance (-21.08% cumulatively), suggesting that the premium income, while steady, was insufficient to offset the losses incurred during downside market movements. The monthly bars reveal a pattern of relatively consistent premium collection punctuated by larger negative payoffs during market corrections. This illustrates the classic "collecting pennies in front of a steamroller" risk profile often associated with selling options - the strategy earns steady income but remains vulnerable to substantial losses during adverse market movements.

Weekly Rolling:
With more frequent rolling, the short put strategy achieves better overall performance, with the return line showing only a slight negative result (-1.46%) by February 2025. Weekly adjustment allows the strategy to mitigate some of the larger drawdowns seen in the monthly approach, though significant negative payoffs still occur (green line reaching -54.78%). Premium income is enhanced (blue line reaching +53.32%), demonstrating how more frequent adjustments can optimize income generation. The component bars reveal a more balanced pattern of small gains and losses, with fewer extreme events compared to the monthly rolling approach. This suggests that increasing rolling frequency helps the strategy better adapt to changing market conditions, providing more opportunities to avoid positions becoming deeply unprofitable during market downturns.

Cross-Strategy Interpretation

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The analysis highlights several key insights across these bullish strategies. First, there's a fundamental risk/reward tradeoff: long calls offer potentially higher returns during strong bullish trends but require paying ongoing premiums, while short puts generate consistent income but face potential large losses during market corrections. The cumulative results across the testing period suggest that long calls outperformed short puts in this particular market environment, which featured significant upward price movement in ETH from January 2024 to February 2025.

Second, rolling frequency significantly impacts performance: weekly rolling enhanced returns for long calls by allowing better capture of price movements, while it improved risk management for short puts by enabling more frequent position adjustments. For both strategies, more frequent rolling created a smoother return profile with fewer extreme outcomes.

Third, the results demonstrate how these strategies complement each other in a portfolio context. Long calls perform best during strong directional uptrends, while short puts excel during periods of modest upward or sideways movement with low volatility. The important outperformance of the weekly-rolled long call strategy (+65.23%) is particularly noteworthy, suggesting that in strongly trending markets, directional option strategies with frequent adjustments can significantly outperform more passive approaches.

Conclusion

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Important Note:
One key factor not accounted for in this analysis is the spread multiplier, which is likely greater than 1x. In fact, observed data shows an average spread multiplier of approximately 1.2x. This implies that, when the spread multiplier is equal to 1, the option premium reflects its theoretical value with no adjustment. However, when the spread multiplier is greater than 1—in our case, 1.2x—this means the actual trading conditions deviate from the theoretical pricing. In this case, buyers pay 20% more than the expected price, making options more expensive to purchase. Conversely, sellers benefit from this spread, earning 20% more than the base premium, which makes selling options more profitable under these conditions.

Future Work

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Several avenues remain open for future exploration. One potential direction involves introducing additional legs—such as spreads, straddles, or protective puts—to build more complex payoff structures that can optimize for skew, convexity, or specific market views within the perpetual options framework. Another promising extension is a cross-asset comparison, applying the current framework to other cryptocurrency pairs to assess the robustness of the observed results. Additionally, extend this comparative study to other chains like Base like we did here to evaluate how gas costs, liquidity depth, and latency impact strategy performance.

Join the growing community of Panoptimists and be the first to hear our latest updates by following us on our social media platforms. To learn more about Panoptic and all things DeFi options, check out our docs and head to our website.

Check out our livestream video on YouTube

Panoptic has explored in prior research how streamia interrelates to implied volatility (IV) for deep out-of-the-money (OTM) Panoption put wings. But what about the opposite side of the options moneyness spectrum? How does IV relate to deep OTM Panoption call wings?

Analyzing call wings is relevant from a risk premia perspective because in certain commodities volatility markets, such as crude oil, it is found that selling call wings carries a higher embedded volatility risk premium (VRP) and accordingly demands more compensation than selling put wings. Both call and put wings inherently contain elevated convexity (potential for explosive payoffs), but does a similar structural asymmetry prevail within crypto volatility markets?

In this article, we will dive into the relative profitability of selling Panoption call wings as well as how the premia of these call wings corresponds with IV.

Results

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The above graphics highlight the monthly premia for selling 10-delta Panoption calls from May 2021 to April 2025 on the ETH/USDC 30bps pools (see code here). The mean monthly premia for this strategy is around 2.8% (39.5% annualized) with the maximum monthly premia of 11.7% (279% annualized) aligning with a subdued Uniswap IV level over the course of July 2022. The collected call wing premia oscillates in an inverse fashion compared to put wing premia the majority of the sample period, while interestingly moving in direct concert with put wing premia at several isolated points when whipsawing price action was taking place.

Note that we assume a 1.2x Panoptic premium to the backtested Uniswap fees based on Panoptic’s historical average since launch.

The above figures display a consistent IV-to-streamia correspondence for 10-delta monthly Panoption call selling as it relates to the WBTC/USDC 30bps pool during an identical sample period and with the same 1.2x spread multiplier being applied. The mean monthly premia for BTC call wing selling of 2.1% (28.5% annualized) is not as attractive as the case for ETH. Akin to the observed properties for Panoption put wing selling, the timing, proportion, and magnitude of premia hikes for selling Panoption call wings also differs from ETH to BTC, but the same general trend persists with both BTC and ETH call wing premia as there is a predominantly inverted relation to put wing premia for both tokens. The highest BTC call wing monthly premia of 6.1% (104% annualized) was also accumulated at the same point during our sample as ETH in July 2022.

Broader Discussion & Conclusions

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The summed premia figures for the 10-delta ETH and BTC monthly call selling strategies show cumulative premia of 114% (21% annualized) and and 85% (16.6% annualized) for the ETH and BTC tactics respectively spanning from May 2021 through April 2025. Over a slightly longer sample, the selling of call wings therefore underperforms the selling of put wings on both the cumulative and average levels for both tokens. But what explains the co-movement of Panoption call wing premia relative to Panoption put wing premia? We look to other asset classes for answers.

In more traditional asset classes such as equities, a resolution of market uncertainty will conventionally lead to what are known as “relief rallies.” For example, the CBOE Volatility Index (VIX) often plunges immediately following Federal Open Market Committee (FOMC) announcements from the Federal Reserve, simultaneously stemming upticks in the underlying equity market returns. The same steep IV index decline is also found to occur in commodities markets such as crude oil and gold subsequent to FOMC announcements. This characteristic specific to equities is reflected in the abnormal trading volume of at-the-money (ATM) call options leading up to FOMC announcements having a positive and statistically significant predictive relationship with index returns in the aftermath of FOMC announcements.

Despite the Uniswap IV being generally muted in times of heightened call wing premia, a similar predictive trait is quantified in BTC markets where BTC returns positively and significantly relate to ATM IV for BTC call options. Macro catalysts (like those pictured above) often spike the Uniswap IV upwards along with Panoption put wing premia, but after sustained episodes of higher Uniswap IV, there are quieter voids where the Uniswap IV diminishes and underlying returns expand. In contrast to crude oil volatility markets, there is a clear structural bias for put wing premia as opposed to call wing premia in the context of Panoptions. The fact remains though that in more peaceful market environments, Panoption call wing premia drifts higher and supplies steady returns in a phenomenon that we dub as the “relief risk premium.”

An excited state for an IV index such as the Uniswap IV portends a wide distribution of forward underlying returns, including relief rallies. As a consequence of the volatility smile, an OTM call option migrating to the status of being ATM imputes a lower overall market IV. It then stands to reason as “Fear-Of-Missing-Out” (FOMO) market dynamics take root, underlying prices rise as implied volatility decreases. BTC and ETH Panoption wings exhibit a solid overall VRP symmetry regardless of a put wing bias, but in the specific case of Panoption call wings, underlying market tranquility (relief risk premium) can be segmented from the market fear (VRP) typically associated with put wings as the climate for generating superior premia.

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