Abstract and Applied Analysis
Volume 2013 (2013), Article ID 682524, 5 pages
http://dx.doi.org/10.1155/2013/682524
Research Article

Homotopy Analysis Method for Boundary-Value Problem of Turbo Warrant Pricing under Stochastic Volatility

Hoi Ying Wong1 and Mei Choi Chiu2

1Department of Statistics, The Chinese University of Hong Kong, Hong Kong
2Department of Mathematics and Information Technology, Hong Kong Institute of Education, Hong Kong

Received 13 December 2012; Accepted 30 January 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Hoi Ying Wong and Mei Choi Chiu. 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

Turbo warrants are liquidly traded financial derivative securities in over-the-counter and exchange markets in Asia and Europe. The structure of turbo warrants is similar to barrier options, but a lookback rebate will be paid if the barrier is crossed by the underlying asset price. Therefore, the turbo warrant price satisfies a partial differential equation (PDE) with a boundary condition that depends on another boundary-value problem (BVP) of PDE. Due to the highly complicated structure of turbo warrants, their valuation presents a challenging problem in the field of financial mathematics. This paper applies the homotopy analysis method to construct an analytic pricing formula for turbo warrants under stochastic volatility in a PDE framework.