Open AccessPricing Exotic Options under a High-Order Markovian Regime Switching Model
Author(s) -
Wai-Ki Ching,
Tak Kuen Siu,
Li-Min Li
Publication year - 2007
Publication title -
journal of applied mathematics and decision sciences
Language(s) - English
Resource type - Journals
eISSN - 1532-7612
pISSN - 1173-9126
DOI - 10.1155/2007/18014
Subject(s) - exotic option , markov process , martingale (probability theory) , valuation of options , economics , valuation (finance) , risk neutral measure , asian option , order (exchange) , path dependent , volatility (finance) , martingale pricing , asset (computer security) , markov chain , econometrics , local martingale , mathematical economics , computer science , finance , mathematics , statistics , machine learning , computer security
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
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