Replica del valor de un pool (CPM) y hedging de perdidas impermanentes

Paper: arXiv 2412.09662

Authors: Agustín Muñoz González, Juan I. Sequeira y Ariel Dembling

Abstract

This article analytically characterizes the impermanent loss for automatic market makers in decentralized exchanges such as Uniswap or Balancer (CPMM). We present a theoretical static replication formula for the pool value using a combination of European calls and puts. We will formulate a result to guarantee coverage for any final price that falls within a predefined range.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a neat theoretical application of Carr-Madan static replication to impermanent loss in CPMMs using discrete long strangles. However, it lacks empirical validation, real historical backtesting with market options data, or consideration of practical constraints like options market liquidity and transaction costs.

Research Flowchart

  flowchart TD
    A[Goal: Characterize Impermanent Loss & Structure Static Hedging for CPMMs] --> B[Inputs: Pool Value Function, European Call & Put Options, Price Range]
    B --> C[Method: Derive Analytical Formula for Impermanent Loss in AMMs]
    C --> D[Process: Construct Static Replication Portfolio using Options]
    D --> E[Outcome: Bounded Risk Coverage Guarantee for Any Price in Predefined Range]