Discrete time hedging with liquidity risk

Abstract

Since it was introduced in 1973, the Black-Scholes hedging strategy has been the standard way to hedge an option under the assumption of liquid market. In a market which is not perfectly liquid, however, the Black-Scholes strategy may not give us an optimal solution because of the liquidity cost. In addition, we cannot revise the hedging portfolio continuously and need to rebalabce in a finite number of times in practice. Without liquidity risk, more rebalancings give a better hedging result. But in illiquid market, it may not be better off since the liquidity cost also increases. In this study, we investigate the relationship among the liquidity cost, hedging error and total risk using Monte-Carlo method.