Hedging in an Illiquid Binomial Market

We analyze numerically the superreplication problem and the associatedhedging strategy in an illiquid binomial market. We prove theexistence of an optimal feedback strategy for European and barrier optionsand compute it numerically by means of a dynamic programmingprinciple. We exhibit that the optimal strategy is not equal to the discretedeltastrategy or to the strategy that minimizes the value function. Theoptimal strategy shows less variability than the discrete-delta strategy orthe strategy consisting of minimizers of the value function due to the effectof liquidity. The performance of these three strategies are assessedby comparing the corresponding wealth processes with the payoff. It isshown that the discrete-delta strategy and the strategy that minimizesthe value function may perform poorly, thus showing the effectiveness ofthe optimal feedback strategy.[...]