About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 246724, 11 pages
http://dx.doi.org/10.1155/2013/246724
Research Article

Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing

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

Received 23 March 2013; Revised 18 May 2013; Accepted 20 May 2013

Academic Editor: T. Diagana

Copyright © 2013 R. Company 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

This paper deals with the numerical solution of option pricing stochastic volatility model described by a time-dependent, two-dimensional convection-diffusion reaction equation. Firstly, the mixed spatial derivative of the partial differential equation (PDE) is removed by means of the classical technique for reduction of second-order linear partial differential equations to canonical form. An explicit difference scheme with positive coefficients and only five-point computational stencil is constructed. The boundary conditions are adapted to the boundaries of the rhomboid transformed numerical domain. Consistency of the scheme with the PDE is shown and stepsize discretization conditions in order to guarantee stability are established. Illustrative numerical examples are included.