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Abstract and Applied Analysis
Volume 2014, Article ID 146745, 9 pages
http://dx.doi.org/10.1155/2014/146745
Research Article

Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing

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

Received 12 December 2013; Revised 3 April 2014; Accepted 6 April 2014; Published 28 April 2014

Academic Editor: Carlos Vazquez

Copyright © 2014 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 presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. Numerical analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive.