Option Pricing for AMM-Native Assets

Westren Capital · 10 August 2026 · 7 min read

Over the past decade, crypto-markets have become more efficient, fragmented, and automated, however, the pricing of derivatives products has not necessarily followed the same evolutionary pace. The majority of option pricing models start from the premise that the underlying has a price process, and liquidity is simply around the price process as the means to execute on it. This premise becomes invalid when the underlying is created and priced by the automated market makers. In this scenario, the liquidity is not merely the place where a trader can execute.

Instead, the liquidity is the component that generates the price. This becomes especially evident in cases of protocol-native assets such as Bittensor subnet tokens.

A transaction with the AMM will affect reserves, reserves will affect the marginal price, and the marginal price will affect the next unit of flow direction for the asset. This process is nonlinear in nature. The same-sized transaction in a very deep pool will have a much smaller impact, while the same transaction made in a shallow pool will result in a significant displacement. In our research of constant-product market maker, an increase in the TAO reserves by 10 percent can be equivalent to an increase in token price by around 21 percent. It is usually referred to as slippage. However, from the options' point of view, this term does not fully describe the situation. In case of the stochastic nature of the incoming flow, the nonlinear dependence between flow and reserves will make the price stochastic as well.

This produces an interesting kind of leverage effect, one that is quite similar but stems from an entirely different source than the classical markets. The closer the price of the token gets to zero in a constant-product pool, the smaller the size of the reserve relative to the transaction value. The same volume of flow thus makes a bigger difference to the price. Volatility goes up as the price declines, not due to the increasing financial leverage of the business, but simply due to the increased sensitivity of the liquidity curve. This is an essential point for the electronic market maker. The tails are not produced by nothing more than investor psychology or a stochastic volatility model.

This means a rethink of how the options surface ought to be conceptualized. A traditional crypto volatility framework would consider spot, implied volatility, maturity, and strike as the key state variables. In the case of an asset native to an AMM, however, one of those variables that will determine the future price distribution is not taken into account. Current pool depth does matter, but so does its dynamics, the level of the flow coming into the pool in relation to the existing liquidity and how concentrated the flow is. Two assets can be characterized by the same spot volatility today, but their option risk can be vastly different due to differences in their liquidity states. One could be trading within a well-established and stable pool, with a dispersed flow. Another could trade in a pool that is less liquid with a portion of all transactions making up a significant part of daily reserve changes.

And herein lies the importance of the difference between liquidity level and liquidity elasticity. The absolute liquidity will give us the amount of liquidity in the pool. The absolute liquidity will not tell us how much volatility there is in the response of the pool to the flow. A pool that is ten times deeper does not automatically mean that it is ten times safer than another one when the flow is also ten times higher. For an EMM desk, the important factor will be the amount of stochastic flow that is absorbed by the liquidity.

This may vary throughout the day and even through time in protocol driven markets.

The AMM as the Source of Volatility

This is most evident in terms of volatility skew. In a constant product AMM, it is natural to have a volatility dynamics process such that when the price decreases, volatility increases. This makes the volatility skew of the implied options surface negative without having to assume an extra stochastic volatility effect. The reason for this is that, even though the ATM behaviour of the two distributions is quite similar, their difference might not be that clear since both can behave very similarly ATM but very differently OTM.

However, for a market maker, such an outcome is of significantly greater importance than a statement like “CEV works better for crypto.” The point is what kind of errors exist. When the errors are skewed towards the wings, a certain surface can seem to be calibrated very accurately when trading, but will constantly undervalue or overvalue the strikes that have significant convexity. The problem becomes crucial especially from the downside perspective. An OTM 20% put might need significantly more implied volatility in the nonlinear AMM setup than its equivalent in the Black-Scholes framework.

Now that has a significant implication for electronic quoting as well. An EMM model should not estimate the whole surface based on ATM volatility and apply the crypto skew for it. Information about the direction and persistence of the skew is already available from the underlying market mechanism. The reaction of the constant-product pool to price movement is one kind of relation. A reaction of a weighted AMM is different. A concentrated liquidity market creates another type of relation due to non-homogenous distribution of liquidity in price space. Thus, the option surface should inherit some information about the underlying mechanism which generates the spot price of the underlying and not assume the underlying asset to be a generic lognormal asset. Bittensor is one of such clean examples, as the market itself is dynamic. In Dynamic TAO, subnet alpha tokens are paired with TAO tokens and traded on the constant-product pools. The protocol may add some TAO and alpha tokens to these pools, making them more liquid with time. This is different from a conventional market maker who simply decides to change his quote size. This is liquidity creation at the protocol level.

This adds another dimension to the valuation of options which can easily be overlooked. While options have an expiration date, it doesn’t mean that the underlying market goes through the entire duration with a constant volatility level. In case there is more liquidity throughout the lifespan of the trade, future flows would be less sensitive to price changes. This means that a three-month option does not automatically equal three months under today’s liquidity level. The proposed framework indicates that rising emissions will lower future integrated variance and compress option prices, especially in cases of longer maturities and shallow liquidity pools.This suggests an interesting way of viewing the protocol emissions. They aren’t just a tokenomics variable, they can also become a volatility variable. The market maker needs to worry not only about the current liquidity level but also about what liquidity the protocol will produce until the option expires.

Now, lets talk about the opposite side of this effect, It is possible to diminish the efficiency of liquidity even if the nominal pool depth remains unchanged. An increase in flow intensity can result in a situation where the same pool will act as if it had much lower depth. Thus, TVL turns out to be a very poor metric when measuring executable liquidity. A pro crypto market maker should understand the amount of flow absorbed by the pool and its concentration. The question is not about "small pool" vs "large pool". It is about the interaction of the pool depth and flow. The issue of distribution of flows makes it crucial. There is no Gaussian distribution of staking and unstaking activities in these markets. The observed flow distribution demonstrates significant excess kurtosis and negative skew, which indicates the presence of abnormal flows and participant asymmetry. The most impressive thing is that "jump days" can form a very low number of observations but generate a very high amount of flow variance. The median proportion of "jump days" is 7.7% per subnet-day in terms of total subnet-days, but they account for a median of 47% of flow variance.

And this alters the significance of volatility for an electronic market maker. Two markets could have identical realized variances but entirely different hedge dynamics. One generates thousands of tiny reserve adjustments. Another stays silent and then sees a single large trade drive its price through multiple volatility regimes before being able to hedge back out. Daily variance does not distinguish between the two. The trading engine does. This is where the importance of the distinction between price risk and liquidity state risk comes into play. It's possible to incur losses without an actual directional move in price just because of a change in the liquidity state. When the pool depth increases dramatically, price becomes less sensitive to movements. The reverse is true when depth is reduced but flows continue. This implies that the option is vulnerable to the development of the market. It is a liquidity Greek, but the more relevant way to view it for an EMM desk is that pool depth is another risk condition that has to be continually marked. Pool depth affects the value of the option, and its effect becomes stronger the shallower the liquidity.

Feedback comes from another channel as well. When dealing on an order book, the market maker is likely able to view their hedge as an exchange with an external liquidity pool. With an AMM, the hedge will affect the reserves and hence the price. Here, the market maker is trading against the very same nonlinear process responsible for the optionality risk. In such a way, a hedge will change the future delta that was meant to be hedged in the first place. That is why execution and valuation cannot be disentangled entirely in AMM native derivatives. The framework provided below illustrates how the replication friction decreases quickly as the pool depth grows.

From Liquidity Risk to Electronic Pricing

At this point, the implications of the above discussion are rather obvious. The issue at hand is not that each option of the Automated Market Maker requires an exotic model to price it. On the contrary, this should not be the case. Once the mechanics of the market dynamics is understood, what is important is the question whether the existing model takes into account the variables that affect its dynamics. Pool depth, flow size, flow concentration, and anticipated growth of liquidity provide more information about the future distribution than any additional layer of complexity to the existing model of spot returns.

This would alter the methodology for assessing opportunity sets within a multi-asset crypto options desk as well. What we do is compare dozens of digital tokens, and sorting them according to their implied volatility or total value locked would overlook the interaction that determines the degree of difficulty involved in hedging such an option position.

It might be much easier to warehouse a token whose implied volatility is 100% and which has a deep and stable liquidity pool compared to another one that has an implied volatility of 70% but which has a shallow liquidity pool, highly concentrated flow, and volatile liquidity. This concept applies even across different maturities. Options that expire in the near future are mostly influenced by the current flow and hedge impact. Longer maturity options, on the other hand, gain a second source of uncertainty since the liquidity environment might have changed by the time the expiry date arrives.

This is especially applicable in the case of crypto, where the distinction between market structure and token economics is becoming more and more blurred. In particular, emissions, incentives for validators and stakers, liquidity programs, and treasury management can all affect the volume and quality of executable liquidity. Within the traditional derivatives framework, this would fall under the category of fundamental information. But for the AMM-native asset, at least some of these factors are important when it comes to understanding the stochastic dynamics of the underlying. What we end up with is a new approach to building the electronic volatility surface. Rather than start from the ATM volatility of today and extrapolate outward, we might choose to start from what we know about the underlying market structure in terms of how it impacts volatility dynamics. And from the flow distribution, we would be able to determine how much additional tail risk premium is necessary, while from the expected liquidity trajectory, we could figure out what portion of the current volatility will remain in the future.

That approach creates a useful separation between model volatility and executable volatility. Model volatility describes the distribution under the assumed dynamics. Executable volatility describes the risk after accounting for the fact that the hedge itself changes the market. In a deep centralized market the distinction may be small. In a shallow AMM it can become the dominant consideration.

Indeed, the most intriguing challenge here is not about creating yet another crypto option pricing framework. Instead, it is about creating an electronic pricing model that understands why crypto tokens have different distributions in the first place. In case of liquidable assets, volatility surface would depend on the liquidity condition. In case of protocol emissions affecting liquidity condition, maturity should account for liquidity development. And in case of whale flows dominating volatility, tail model should be adjusted for concentration rather than using only historical standard deviation. This is the future of crypto market making envisioned by Westren Capital. The future generation of electronic market makers would have to price the underlying market dynamics along with the asset itself. Liquidity would become an element that needs to be forecasted and managed rather than just monitored on the dashboard. So, in case of AMM option pricing, the key question changes. It is not enough to know the token’s current volatility anymore. The pertinent issue is to identify what liquidity condition will cause the volatility of the token tomorrow, how it evolves if the price changes, how the dynamics of the protocol modify it during the lifespan of the option and what happens if the market maker itself intervenes.

This is the true difference between option pricing on crypto assets and option pricing on crypto markets. For an AMM-native asset, the market is part of the underlying