A General Accurate Approximation for Pricing and Hedging Basket Options with Exact Moment Matching

Abstract

This article provides a new methodology for pricing and hedging basket options. The authors approximate the basket by using the shifted log-normal distribution with the polynomial expansion, which can match exactly any required m moments of the basket, to give quasi-analytical formulas for the prices and hedging parameters of basket options. Numerical simulations show that the methodology provides superior results for basket option prices and hedging parameters. This methodology works well not only for regular baskets but also for negative-weight baskets and negative-value baskets. Compared with the best available methods, the authors’ methodology appears to perform better.