Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes

In this paper, a new approach is proposed to construct willow tree (WT) for generalized hyperbolic (GH) Lévy processes. There are two advantages of our proposed approach compared to the classical WT methods. Firstly, it avoids the moments matching from Johnson curve in the known WT construction. Secondly, the error of European option pricing is only determined by time partition ∆t under some conditions. Since the moments of Lévy measure are removed from this algorithm, our approach improves the stability and accuracy of WT in option pricing. Numerical experiments support our claims. Moreover, the new approach can be extended to other Lévy processes if their characteristic functions are expressed by explicit forms.