Explicit option valuation in the exponential NIG model

Abstract

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential Lévy model driven by the normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric models, and take the form of simple and quickly convergent series, under some conditions involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier and Fast Fourier transforms, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.