Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance).Fakharany, MMRE.; Company Rossi, R.; Jódar Sánchez, LA. (2015). Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems. Journal of Applied Mathematics. 2015:1-10. https://doi.org/10.1155/2015/960728S110201