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The Price of Liquidity: Implied Volatility of Automated Market Maker Fees

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  • Maxim Bichuch
  • Zachary Feinstein

Abstract

An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as a market maker. Within this work, we reinterpret the loss-versus-rebalancing as the implied fee stream generated by an AMM so that a risk-neutral investor is indifferent in the decision of providing liquidity. With this implied fee structure, we propose a novel fixed-for-floating swap on the fees generated by an AMM in order to quote the implied volatilities and implied correlations of digital assets. We apply this theory to realized fees in different markets to empirically validate the relevance of the deduced fee-based volatility.

Suggested Citation

  • Maxim Bichuch & Zachary Feinstein, 2025. "The Price of Liquidity: Implied Volatility of Automated Market Maker Fees," Papers 2509.23222, arXiv.org.
    • Handle: RePEc:arx:papers:2509.23222
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    File URL: http://arxiv.org/pdf/2509.23222
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    References listed on IDEAS

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    1. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    2. Leonardo Baggiani & Martin Herdegen & Leandro S'anchez-Betancourt, 2025. "Optimal Dynamic Fees in Automated Market Makers," Papers 2506.02869, arXiv.org, revised Jun 2025.
    3. Xue Dong He & Chen Yang & Yutian Zhou, 2024. "Optimal Design of Automated Market Makers on Decentralized Exchanges," Papers 2404.13291, arXiv.org, revised Nov 2024.
    4. Bent Jesper Christensen & Charlotte Strunk Hansen, 2002. "New evidence on the implied-realized volatility relation," The European Journal of Finance, Taylor & Francis Journals, vol. 8(2), pages 187-205, June.
    5. Eric Budish & Peter Cramton & John Shim, 2014. "Implementation Details for Frequent Batch Auctions: Slowing Down Markets to the Blink of an Eye," American Economic Review, American Economic Association, vol. 104(5), pages 418-424, May.
    6. Philippe Bergault & S'ebastien Bieber & Leandro S'anchez-Betancourt, 2025. "Optimal Exit Time for Liquidity Providers in Automated Market Makers," Papers 2509.06510, arXiv.org, revised Oct 2025.
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    Cited by:

    1. Leonardo Baggiani & Martin Herdegen & Leandro Sanchez-Betancourt, 2026. "Competition between DEXs through Dynamic Fees," Papers 2603.09669, arXiv.org.
    2. Jimmy Risk & Shen-Ning Tung & Tai-Ho Wang, 2026. "Pricing and hedging for liquidity provision in Constant Function Market Making," Papers 2603.01344, arXiv.org.

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