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Option pricing and Esscher transform under regime switching
Authors:Email author" target="_blank">Robert J?ElliottEmail author  Leunglung?Chan  Tak Kuen?Siu
Institution:(1) Haskayne School of Business, University of Calgary, Calgary, Alberta, CANADA;(2) Department of Mathematics and Statistics, University of Calgary, CANADA;(3) Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK
Abstract:Summary We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara 33], we can justify our pricing result by the minimal entropy martingale measure (MEMM).We would like to thank the referees for many helpful and insightful comments and suggestions.Correspondence to: R. J. Elliott
Keywords:Option pricing  Regime switching  Hidden Markov chain model  Esscher transform  MEMM
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