Lorenzo Schoenleber (Collegio Carlo Alberto)

The Expected Impermanent Loss in Decentralized Liquidity Provision: Cross-Sectional Evidence from Crypto Options

Abstract. We propose a continuous-time stochastic model to analyze the dynamics of impermanent loss in liquidity pools in decentralized finance (DeFi) protocols. We replicate the impermanent loss using option portfolios for the individual tokens. We estimate the risk-neutral joint distribution of the tokens by minimizing the Hansen–Jagannathan bound, which we then use for the valuation of options on relative prices and for the calculation of implied correlations. In our analyses, we investigate the relationship between the impermanent loss, the implied quantities, and their risk premia in the cross-section of liquidity pools. We test our theory using options data from a major centralized derivative exchange.