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.

我们在由正常逆高斯过程驱动的指数 Lévy 模型中为各种路径无关选项提供封闭形式的定价公式。结果在对称和非对称模型中均获得，并且在涉及对数远期货币性和工具成熟度的某些条件下采用简单且快速收敛的级数形式。证明基于 Mellin 空间中任意路径无关支付的价格的分解表示以及来自复杂分析的工具。由于与标准数值方法（傅立叶和快速傅立叶变换、蒙特卡洛模拟）对实际参数集进行了多次比较，评估了结果的有效性。还提供了收敛速度和截断误差的精确界限。