Hedging in an illiquid binomial market

We analyze numerically the superreplication problem and the associated hedging strategy in an illiquid binomial market. We prove the existence of an optimal feedback strategy for European and barrier options and compute it numerically by means of a dynamic programming principle. We exhibit that the optimal strategy is not equal to the discrete-delta strategy or to the strategy that minimizes the value function. The optimal strategy shows less variability than the discrete-delta strategy or the strategy consisting of minimizers of the value function due to the effect of liquidity. The performance of these three strategies are assessed by comparing the corresponding wealth processes with the payoff. It is shown that the discrete-delta strategy and the strategy that minimizes the value function may perform poorly, thus showing the effectiveness of the optimal feedback strategy.