A new radial basis functions method for pricing American options under Merton's jump-diffusion model

Abstract

A new radial basis functions (RBFs) algorithm for pricing financial options under Merton's jump-diffusion model is described. The method is based on a differential quadrature approach, that allows the implementation of the boundary conditions in an efficient way. The semi-discrete equations obtained after approximation of the spatial derivatives, using RBFs based on differential quadrature are solved, using an exponential time integration scheme and we provide several numerical tests which show the superiority of this method over the popular Crank–Nicolson method. Various numerical results for the pricing of European, American and barrier options are given to illustrate the efficiency and accuracy of this new algorithm. We also show that the option Greeks such as the Delta and Gamma sensitivity measures are efficiently computed to high accuracy.

Keywords:

• Lévy processes
• jump-diffusion models
• American options
• radial basis
• differential quadrature
• exponential time integration

2010 AMS Subject Classifications::

• 65M70
• 62P05
• 91G20

Acknowledgements

The authors thank all the referees and the editors for their constructive remarks which considerably strengthened the work contained in this paper. The research of A.A.E.F. Saib was supported by a postgraduate research scholarship from the Tertiary Education Commission and the University of Mauritius.