European Option Pricing with Liquidity Shocks

TL;DR

This paper analyzes European option pricing under liquidity shocks using a regime-switching model, deriving semi-linear PDEs for indifference prices, and provides numerical insights into liquidity risk premia for better valuation and hedging strategies.

Contribution

It introduces a regime-switching framework for option valuation under liquidity shocks and derives semi-linear PDEs for indifference prices, including asymptotic analysis and numerical studies.

Findings

Semi-linear PDEs characterize indifference prices under liquidity shocks.

Asymptotic analysis reveals effects of small liquidity shock probabilities.

Numerical results offer practical guidelines for liquidity risk adjustment.

Abstract

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled HJB equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.