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DeFi Arbitrage in Hedged Liquidity Tokens

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  • Maxim Bichuch
  • Zachary Feinstein

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.

Suggested Citation

  • Maxim Bichuch & Zachary Feinstein, 2024. "DeFi Arbitrage in Hedged Liquidity Tokens," Papers 2409.11339, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2409.11339
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    References listed on IDEAS

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    3. Stefan Loesch & Nate Hindman & Mark B Richardson & Nicholas Welch, 2021. "Impermanent Loss in Uniswap v3," Papers 2111.09192, arXiv.org.
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    5. Jin Hong Kuan, 2022. "Liquidity Provision Payoff on Automated Market Makers," Papers 2209.01653, arXiv.org.
    6. Harris, Lawrence, 1986. "A transaction data study of weekly and intradaily patterns in stock returns," Journal of Financial Economics, Elsevier, vol. 16(1), pages 99-117, May.
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