Narrow Results

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.

This paper examines the impact of banks’ lending incentives on asset prices and bank cash holdings under liquidity risk. Banks make lending decisions based on the tradeoff between costs (fire sales of illiquid assets) and benefits (high returns from bank loans). This paper shows fire sales of assets can be an endogenous outcome, even if banks are endowed with enough cash to meet liquidity shocks. This paper also helps explain why banks have kept a large amount of cash without lending after government capital injections in the 2008 financial crisis. The model further provides policy implications for government intervention.