Optimal Discrete Hedging in Garman-Kohlhagen Model with Liquidity Risk

In this paper, we study a discrete time hedging and pricing problem using Garman-Kohlhagen model in a market with liquidity costs. We prove that delta hedging is an unique optimal strategy. In particular, the hedging strategy will have expected hedging error is the infinitesimal of the length of the revision interval with order of 3/2. An implicit finite difference method is presented and showed to be stable for solving the PDE required to obtain the option price. Finally, some experiments illustrate the efficiency of our method.