Liquidity Provider Returns and Derivative Replication in Geometric Mean AMMs

Summary

The document studies liquidity provider (LP) returns in geometric mean market makers, including pools with weights that change over time or vary stochastically. It develops expressions for LP share returns and their no-arbitrage prices, extending results that apply to constant-weight pools.

Using these relationships, the paper describes how to configure pools so LP shares reproduce derivative payoffs. The resulting hedges are model-independent and exact when a contract’s payoff meets an elasticity condition; standard options are among the examples. The approach also shows how passive LP positions can represent some active trading strategies. The document gives theoretical claims rather than empirical performance evidence, and the stated replication result is limited to payoffs satisfying the specified condition.

Key ideas

• The analysis extends LP return and pricing results to geometric mean pools with changing or stochastic weights.
• LP shares can replicate derivative payoffs when the payoff function satisfies an elasticity constraint.
• The proposed replication is model-independent and exact under that constraint.
• Standard options and some active trading strategies are cited as possible replicated payoffs.

Tags

# Liquidity Provider Returns in Geometric Mean Markets


# Liquidity Provider Returns in Geometric Mean Markets









Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean. This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights. These results include the returns and no-arbitrage prices of liquidity pool (LP) shares that investors receive for supplying liquidity to G3Ms. Using these expressions, we show how to create G3Ms whose LP shares replicate the payoffs of financial derivatives. The resulting hedges are model-independent and exact for derivative contracts whose payoff functions satisfy an elasticity constraint. These strategies allow LP shares to replicate various trading strategies and financial contracts, including standard options. G3Ms are thus shown to be capable of recreating a variety of active trading strategies through passive positions in LP shares.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.