OPTION REPLICATION IN DISCRETE TIME WITH THE COST OF ILLIQUIDITY

We introduce a model of liquidity risk through a stochastic supply curve for price taking traders. The supply curve gives the actual execution cost investors face in trading assets. We use the solutions to the modified Black-Scholes type PDE and obtain the delta-hedging strategies. We then show the replicating portfolio including liquidity costs converges to the payoff of the option. We demonstrate the replication error of discrete-time trading strategy decreases with inhomogeneous rebalancing times, and investigate an optimal positioning of them.