Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Abstract

In this paper we employ a one-factor Levy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basket with an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr–Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Levy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Levy correlation by matching model and market prices for basket options. Our main finding is that the implied Levy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) at-the-money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Levy correlation.