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Type: Journal article
Title: Option pricing for GARCH models with Markov switching
Author: Elliott, R.
Siu, T.
Chan, L.
Citation: International Journal of Theoretical and Applied Finance, 2006; 9(6):825-841
Publisher: World Scientific Publishing Co Pte Ltd
Issue Date: 2006
ISSN: 0219-0249
Statement of
Robert J. Elliott; Tak Kuen Siu; Leunglung Chan
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.
Rights: © World Scientific Publishing Company
DOI: 10.1142/S0219024906003846
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Appears in Collections:Applied Mathematics publications
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