TL;DR: Constant volatility AMMs requires the fee rate to change at every txn. By computing the fee on a per-trade basis in Uniswap, it is possible to target a constant volatility (eg. 100% annualized) regardless of the actual price dynamics of the underlying assets. Trading assets in a constant volatility…

Gamma is a measure of the convexity of an asset’s payoff curve squeeth is a blockchain-native asset with a payoff where gamma = +2 at all prices Single-tick Uniswap v3 LP positions can be used to hedge the gamma of payoff curves with positive convexity like squeeth We demonstrate how…

TL;DR: Providing liquidity in Uniswap is limited to taking directional positions with “positive delta.” This means LPs will not benefit from participating in bearish token pools. Protocols like Euler Finance allows users to incorporate short positions into their strategies. Combining a short position with Uniswap v2 or v3 LP…

TL;DR: In this post, I show how to use the daily volumes and liquidity information directly from Uniswap v3 pools to extract the implied volatility of any asset. In my last post, I demonstrated that it may be more profitable to lend a Uni v3 LP position as an option…

TL;DR — Uni v3 LP positions can be decomposed into a short put payoff and a range component. The value of a Uni v3 position is the sum of 1) a short put, whose value is given by the Black-Scholes model, and 2) a range term, whose closed-form expression is found using…

TL;DR: The expected impermanent loss in constant product AMMs like Uniswap and SushiSwap follows a simple expression that depends on the volatility σ and drift μ of the asset. Specifically, the expected IL is the worst for assets which have a large annual drift μ, while the impact of price…

This is the second article in a series of medium posts about choosing and managing Uniswap v3 LP positions. Read part 1 here. TL;DR: Uni v3 liquidity positions have to balance capital efficiency and the time spent in-the-money. The product of these two effects results in a simple √T dependence…

TL;DR Perpetual Uniswap v3 Options can be deployed right now between any two assets (think beyond stablecoin-token pairs), for any expiration time (not just 1DTE), at any delta (not just ATM), and without the need to deploy an intermediary protocol. In my previous post, I described how Uniswap v3 LP…

TL;DR: the probability that a LP position centered between an upper tick tH and a lower tick tL will end up within that range (ie. be In-The-Money) after a time T is: