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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 517480, 11 pages
http://dx.doi.org/10.1155/2013/517480
Research Article

Positive Solutions of European Option Pricing with CGMY Process Models Using Double Discretization Difference Schemes

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

Received 30 May 2013; Revised 18 September 2013; Accepted 6 October 2013

Academic Editor: Fabio M. Camilli

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 analysis of PIDE option pricing models with CGMY process using double discretization schemes. This approach assumes weaker hypotheses of the solution on the numerical boundary domain than other relevant papers. Positivity, stability, and consistency are studied. An explicit scheme is proposed after a suitable change of variables. Advantages of the proposed schemes are illustrated with appropriate examples.