OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING

Robert J. Elliott (), Tak Kuen Siu and Leunglung Chan ()
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Robert J. Elliott: Haskayne School of Business, University of Calgary, T2N 1N4 Calgary, Canada
Leunglung Chan: Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 06, 825-841

Abstract: In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters.

Keywords: Markov switching conditional Esscher transform; Markov switching Heston-Nandi's GARCH model; recursive formula; analytical option valuation (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S0219024906003846

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