Basket option pricing and implied correlation in a Lévy copula model

In this paper we employ the L´evy copula model to determine basket option prices. More precisely, basket option prices are determined by replacing 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. Two approaches are considered. In the first approach, we replace the arithmetic sum by an appropriate geometric sum, whereas the second approach can be considered as a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several L´evy models are calibrated to market data and basket option prices are determined. In a last part we show how our newly designed basket option pricing formula can be used to define implied L´evy correlation by matching model and market prices for basket options. Our main finding is that the implied L´evy 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 L´evy correlation.status: publishe