Automated market makers for negative prices: The impact of market depth and impermanent loss on liquidity provider profitability

Abstract

This thesis investigates the design of automated market makers (AMMs) for trading tokenized derivatives in decentralized finance. Motivated by the limitations of existing AMMs, which only permit strictly positive prices, we introduce an invariant that also allows for negative prices. As a primary use case, the thesis develops an AMM for trading an offset token against tokenized euros. The thesis employs, on the one hand, a Monte Carlo–based simulation to evaluate the risk-adjusted returns of an AMM. The simulation includes two types of traders: arbitrage traders, who exploit price deviations between the AMM and the fair value, and noise traders, who represent demand for liquidity. On the other hand, we introduce KPIs such as impermanent loss and market depth. The goal of the thesis is to analyse whether these KPIs can be used to predict the risk-adjusted returns of an AMM.