The Pricing And Hedging Of Constant Function Market Makers∗

Abstract

We investigate the most common type of blockchain-based decen- tralized exchange, which are known as constant function market makers (CFMMs). We examine the the market microstructure around CFMMs and present a model for valuing the liquidity provider (LP) mechanism and estimating the value of the associated derivatives. We develop a model with two types of traders that have different information and contribute methods for simulating the behavior of each trader and ac- counting for trade PnL. We also develop ideas around the equilibrium distribution of fair price conditional on the arrival of traders. Finally, we show how these findings might be used to think about parameters for alternative CFMMs.