Optimal Hedging of Options with Transaction Costs

One of the most successful approaches to option hedging with transaction costs is the utility based approach, pioneered by Hodges and Neuberger (1989). Judging against the best possible tradeoff between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. Since the knowledge of the optimal hedging strategy is of great practical significance, in this paper we suggest and implement two methods for finding the optimal hedging strategy with transaction costs. The first method is the approximation of the utility based hedging strategy which yields a closed-form solution. The second method is the optimization of the parameters of the hedging strategy in some risk-return space. We provide an empirical testing of our hedging strategies against the asymptotic and some other well-known strategies and find that our strategies outperforms all the others.