Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

الملخص EN

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stableprocess known as CGMY model.

A doublediscretization finite difference scheme is used for the treatmentof the unbounded nonlocal integral term.

We also introduce in thescheme the Patankar-trick to guarantee unconditional nonnegativenumerical solutions.

Integration formula of open type is used inorder to improve the accuracy of the approximation of the integralpart.

Stability and consistency are also studied.

Illustrative examples are included.