Optimal Hedging of Option Portfolios with Transaction Costs

Abstract

One of the most successful approaches to option hedging with transaction costs is the utility based approach pioneered by Hodges and Neuberger (1989). However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. The direct numerical computations of the utility based hedging strategy are cumbersome in a practical implementation. Despite some recent advances in finding an explicit description of the utility based hedging strategy by using either asymptotic, approximation, or other methods, so far they were concerned primarily with hedging a single plain-vanilla option. However, in practice one often faces the problem of hedging a portfolio of options on the same underlying asset. Since the knowledge of the optimal hedging strategy for a portfolio of options is of great practical significance, in this paper we suggest a simplified parameterized description of the utility based hedging strategy for a portfolio of options and a simple method for finding the optimal parameters. We provide an empirical testing of our optimized hedging strategies against some alternative strategies and show that our strategies outperform all the others.