Dynamic hedging of basket options under proportional transaction costs using receding horizon control

Abstract

In this article, we develop a semi-definite programming-based receding horizon control approach to the problem of dynamic hedging of European basket call options under proportional transaction costs. The hedging problem for a European call option is formulated as a finite horizon constrained stochastic control problem. This allows us to develop a receding horizon control approach that repeatedly solves semi-definite programmes on-line in order to dynamically hedge. This approach is competitive with Black–Scholes delta hedging in the one-dimensional case with no transaction costs, but it also applies to multi-dimensional options such as basket options, and can include transaction costs. We illustrate its effectiveness through a numerical example involving an option on a basket of five stocks.