Discrete time hedging with liquidity risk

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland's discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283-1301], we consider a discrete time version of the Black-Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modified option hedging strategy which depends on the size of the parameter for liquidity risk. We also discuss an analytic method of solving the pricing equation using a series solution.

► This study provides discrete time pricing and hedging strategy in a market with liquidity cost. ► It gives more realistic discrete hedging strategy in an illiquid market. ► We find the hedging strategy that makes the expected hedging error 0 using Leland scheme. ► We provide an analytical approximation method to solve the pricing PDE. ► We provide a numerical example to show that our hedging strategy has the desired property.