Option Pricing Under Generalized Hyperbolic Lévy Model And Its Empirical Study

As one of the theoretical system of modern finance, option pricing embodies many of financial theory core issues. The reasonable pricing can provide indispensable theoretical basis for investors with investment strategies and the investment risk control. Therefore, it has a very important theoretical and realistic significance. The reasonable hypothesis (incomplete markets) and the return distribution are the important foundation in option pricing. This paper is mainly using generalized hyperbolic Lévy process in place of Brownian motion to price the European option. In order to get the numerical solution, we use Quasi-Monte Carlo methods, and use moment estimation method to estimate the parameters of generalized hyperbolic distribution density.Finally, we make some empirical studies and the results show that the generalized hyperbolic distribution is better than the normal distribution in fitting the return of assets, and the price we get under the GH Lévy model is more close to the real price than the price under the BS model.