This thesis presents the NIG-model and methods for its computational implementation for option pricing using the Monte-Carlo method. The NIG-model is a stock price model which uses a geometric Normal Inverse Gaussian (NIG) Lévy Process. An introduction to the NIG distribution and Lévy Processes is included and some advantages compared to the Black-Scholes model are discussed. Afterwards methods for random number sampling, from linear congruent random number generators to methods for generating Normal, Inverse Gaussian and Normal Inverse Gaussian random numbers, are shown. The method of moments is introduced for calibrating the NIG-model to empirical data and the Esscher transformation is presented for finding a suitable martingale measure. Finally, the presented methods are used to price a European call option on the German stock SGL Carbon SE Inhaberaktie by Monte-Carlo while discussing some of the entailing difficulties.      «

This thesis presents the NIG-model and methods for its computational implementation for option pricing using the Monte-Carlo method. The NIG-model is a stock price model which uses a geometric Normal Inverse Gaussian (NIG) Lévy Process. An introduction to the NIG distribution and Lévy Processes is included and some advantages compared to the Black-Scholes model are discussed. Afterwards methods for random number sampling, from linear congruent random number generators to methods for generating N...     »