Pool Value Replication (CPM) and Impermanent Loss Hedging

Agustin Mu\~noz Gonzalez, Juan Ignacio Sequeira and Ariel Dembling

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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.

Date: 2025-03
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