Pricing Exotic Options under a High-Order Markovian Regime Switching Model. (8th October 2007)

• Record Type: Journal Article
• Authors: Ching, Wai-Ki; Siu, Tak-Kuen; Li, Li-Min
• Other Names: Wong Wing-Keung Academic Editor.
• Is Part Of: Journal of applied mathematics & decision sciences. Volume 2007(2007)
• Publication Date: 2007-10-08
• Subjects: Operations research -- Periodicals; Mathematical models -- Periodicals; Statistics -- Periodicals; Quality control -- Periodicals; Mathematical models; Operations research; Quality control; Statistics; Periodicals; 519.05
• DOI: 10.1155/2007/18014
• Languages: English
• ISSNs: 1173-9126

Abstract

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.