PinnedUniswap V3 LP Tokens as Perpetual Put and Call OptionsUPDATE: See the following follow-up articles on Uniswap v3 Perpetual options: Synthetic Options and Short Calls in Uniswap V3 How to create perpetual options in Uniswap v3 Last month, Uniswap released version 3 of their automated market making (AMM) protocol. A major improvement in Uniswap v3 is the ability for…Uniswap7 min readUniswap7 min read

Apr 4, 2022Designing a constant volatility AMMTL;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…Defi9 min readDefi9 min read

Feb 23, 2022Gamma transforms: How to hedge squeeth using Uni V3Gamma 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…Defi8 min readDefi8 min read

Jan 12, 2022How to deploy delta-neutral liquidity in Uniswap — or why Euler Finance is a game changer for liquidity providersTL;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 tokens…Uniswap10 min readUniswap10 min read

Nov 21, 2021On-chain Volatility and Uniswap v3TL;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…Uniswap6 min readUniswap6 min read

Oct 17, 2021Pricing Uniswap v3 LP Positions: Towards a New Options Paradigm?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…Ethereum11 min readEthereum11 min read

Oct 1, 2021Calculating the Expected Value of the Impermanent Loss in UniswapTL;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. …Uniswap5 min readUniswap5 min read

Sep 15, 2021A Guide for Choosing Optimal Uniswap V3 LP Positions, Part 2This 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…Uniswap8 min readUniswap8 min read

Aug 24, 2021How to Create Perpetual Options in Uniswap v3TL;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…Uniswap8 min readUniswap8 min read

Aug 4, 2021A Guide for Choosing Optimal Uniswap V3 LP Positions, Part 1TL;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:Uniswap8 min readUniswap8 min read