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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 369795, 16 pages
http://dx.doi.org/10.1155/2014/369795
Research Article

Pricing American Options Using a Nonparametric Entropy Approach

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
2Australian School of Business, University of New South Wales, NSW 2052, Australia

Received 4 February 2014; Accepted 7 March 2014; Published 8 May 2014

Academic Editor: Fenghua Wen

Copyright © 2014 Xisheng Yu and Li Yang. 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 studies the pricing problem of American options using a nonparametric entropy approach. First, we derive a general expression for recovering the risk-neutral moments of underlying asset return and then incorporate them into the maximum entropy framework as constraints. Second, by solving this constrained entropy problem, we obtain a discrete risk-neutral (martingale) distribution as the unique pricing measure. Third, the optimal exercise strategies are achieved via the least-squares Monte Carlo algorithm and consequently the pricing algorithm of American options is obtained. Finally, we conduct the comparative analysis based on simulations and IBM option contracts. The results demonstrate that this nonparametric entropy approach yields reasonably accurate prices for American options and produces smaller pricing errors compared to other competing methods.