Abstract and Applied Analysis
Volume 2012 (2012), Article ID 120358, 20 pages
http://dx.doi.org/10.1155/2012/120358
Research Article

Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models

M.-C. Casabán, R. Company, L. Jódar, and J.-V. Romero

Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Received 10 September 2012; Revised 7 November 2012; Accepted 7 November 2012

Academic Editor: Carlos Vazquez

Copyright © 2012 M.-C. Casabán et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new discretization strategy is introduced for the numerical solution of partial integrodifferential equations appearing in option pricing jump diffusion models. In order to consider the unknown behaviour of the solution in the unbounded part of the spatial domain, a double discretization is proposed. Stability, consistency, and positivity of the resulting explicit scheme are analyzed. Advantages of the method are illustrated with several examples.