Paper: arXiv 2503.21967

Authors: Agustin Muñoz Gonzalez, Juan Ignacio Sequeira, Ariel Dembling

Abstract

This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool’s value using a combination of European calls and puts. Furthermore, we establish a result guaranteeing hedging coverage for all final prices within a predefined interval. These theoretical results motivate a numerical example where we illustrate the strangle strategy using real cryptocurrency options data from Deribit, one of the most liquid markets available.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a solid mathematical framing of automated market maker (AMM) payoffs and impermanent loss replication using European options. However, it relies predominantly on well-established theoretical option replication methods (Ross, Breeden-Litzenberger) with limited empirical backtesting beyond basic illustrative examples.

Research Flowchart

  flowchart TD
    A[Goal: Characterize & Hedge Impermanent Loss in AMMs] --> B[Derive Static Replication Formula using Calls & Puts]
    B --> C[Establish Price Interval Coverage Guarantee]
    D[Input: Deribit Options Data & ETH/USD Prices] --> E[Construct & Price Strangle Hedging Strategy]
    C --> E
    E --> F[Outcomes: Validated IL Hedging & Exact Portfolio Weights]

Cited References (15)

  1. Towards a theory of volatility trading (2001)
  2. Options and efficiency (1976)
  3. Prices of state-contingent claims implicit in option prices (1978)
  4. An analysis of Uniswap markets (2019) — link
  5. The replicating portfolio of a constant product market (2020)
  6. Spanning and completeness in markets with contingent claims (1987)
  7. Spanning and completeness with options (1988)
  8. Delta function and Heaviside function (2015)
and 7 more
  1. All about the Dirac delta function ? (2003)
  2. 0x: An open protocol for decentralized exchange on the Ethereum blockchain (2017)
  3. Bancor protocol (2017)
  4. Formal specification of constant product (xy= k) market maker model and implementation (2018)
  5. Relation between bid–ask spread, impact and volatility in order-driven markets (2008)
  6. Ethereum: a secure decentralised generalised transaction ledger (2014) (2017)
  7. Combinatorial information market design (2003)

0 of 15 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.