Pricing of Basket Options Using Univariate Normal Inverse Gaussian Approximations

In this paper we study the approximation of a sum of assets having marginal logreturns being multivariate normal inverse Gaussian distributed. We analyse the choice of a univariate exponential NIG distribution, where the approximation is based on matching of moments. Probability densities and European basket call option prices of the two-asset and univariate approximations are studied and analyzed in two cases, each case consisting of 9 scenarios of different volatilities and correlations, to assess the accuracy of the approximation. We find that the sum can be well approximated, however, failing to match the tails for some extreme parameter choices. The approximated option prices are close to the true ones, although becoming significantly underestimated for far out-of-the-money call options.