  We provide closed-form pricing formulas for a wide variety of
path-independent options, in the exponential L\'evy model driven by the Normal
inverse Gaussian process. The results are obtained in both the symmetric and
asymmetric model, and take the form of simple and quickly convergent series,
under some condition 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.
