{"title":"DeFi Arbitrage in Hedged Liquidity Tokens","authors":"Maxim Bichuch, Zachary Feinstein","doi":"arxiv-2409.11339","DOIUrl":null,"url":null,"abstract":"Empirically, the prevailing market prices for liquidity tokens of the\nconstant product market maker (CPMM) -- as offered in practice by companies\nsuch as Uniswap -- readily permit arbitrage opportunities by delta hedging the\nrisk of the position. Herein, we investigate this arbitrage opportunity by\ntreating the liquidity token as a derivative position in the prices of the\nunderlying assets for the CPMM. In doing so, not dissimilar to the\nBlack-Scholes result, we deduce risk-neutral pricing and hedging formulas for\nthese liquidity tokens. Furthermore, with our novel pricing formula, we\nconstruct a method to calibrate a volatility to data which provides an updated\n(non-market) price which would not permit arbitrage if quoted by the CPMM. We\nconclude with a discussion of novel AMM designs which would bring the pricing\nof liquidity tokens into the modern financial era.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Risk Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11339","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Empirically, the prevailing market prices for liquidity tokens of the
constant product market maker (CPMM) -- as offered in practice by companies
such as Uniswap -- readily permit arbitrage opportunities by delta hedging the
risk of the position. Herein, we investigate this arbitrage opportunity by
treating the liquidity token as a derivative position in the prices of the
underlying assets for the CPMM. In doing so, not dissimilar to the
Black-Scholes result, we deduce risk-neutral pricing and hedging formulas for
these liquidity tokens. Furthermore, with our novel pricing formula, we
construct a method to calibrate a volatility to data which provides an updated
(non-market) price which would not permit arbitrage if quoted by the CPMM. We
conclude with a discussion of novel AMM designs which would bring the pricing
of liquidity tokens into the modern financial era.
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