EUROPEAN OPTION PRICING WITH LIQUIDITY SHOCKS
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 Hamilton–Jacobi–Bellman (HJB) equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. A comparative analysis between the model price and the classical Black–Scholes benchmark is given using the concepts of implied and adjusted time to maturity. 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.