Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 18014, 15 pages
doi:10.1155/2007/18014
Research Article
Pricing Exotic Options under a High-Order Markovian Regime Switching Model
1Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
2Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Received 25 September 2006; Revised 14 March 2007; Accepted 7 August 2007
Academic Editor: Wing-Keung Wong
Copyright © 2007 Wai-Ki Ching 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
We consider the pricing of exotic options when the price dynamics of the underlying
risky asset are governed
by a discrete-time Markovian regime-switching process driven by an observable, high-order
Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility
of the underlying risky asset's return switch over time according to the states of the
HOMM, which are interpreted as the states of an economy. We will then employ the well-known
tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale
measure for option valuation. Moreover, we will also investigate the impact of the high-order
effect of the states of the economy on the prices of some path-dependent exotic options, such
as Asian options, lookback options, and barrier options.