Optimal hedging of basket options using smooth payoff functions: Comparison with super-hedging strategy

In this paper, we consider a mean-variance optimal hedging problem for a European-style basket option using individual options with arbitrarily smooth payoff functions. To this end, we investigate theoretical properties for the smooth functions of hedging basket options, and show that (i) the optimal smooth functions for the put option may be constructed using those for the call option (and vice versa) and that (ii) delta in the replicating portfolio may be computed efficiently. Then, we compare the optimal hedges with super-hedging strategy. Our numerical experiment illustrates that the optimal hedging strategy is better if we take standard deviation as a performance measure of the hedge, whereas for the worst case error, super-hedging tends to provide a better bound with a given confidence level.