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Option Pricing For Garch Models With Markov Switching

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Author Info

  • ROBERT J. ELLIOTT

    () (Haskayne School of Business, University of Calgary, T2N 1N4 Calgary, Canada)

  • TAK KUEN SIU

    () (Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EH14 4AS Edinburgh, UK)

  • LEUNGLUNG CHAN

    () (Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Canada)

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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 09 (2006)
Issue (Month): 06 ()
Pages: 825-841

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Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:06:p:825-841

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Related research

Keywords: Markov switching conditional Esscher transform; Markov switching Heston-Nandi's GARCH model; recursive formula; analytical option valuation;

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Cited by:
  1. Bertholon, H. & Monfort, A. & Pegoraro, F., 2008. "Econometric Asset Pricing Modelling," Working papers 223, Banque de France.
  2. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
  3. A. Thavaneswaran & Jagbir Singh, 2010. "Option pricing for jump diffusion model with random volatility," Journal of Risk Finance, Emerald Group Publishing, vol. 11(5), pages 496-507, November.
  4. Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 99-107, August.
  5. Kiyotaka Satoyoshi & Hidetoshi Mitsui, 2011. "Empirical Study of Nikkei 225 Options with the Markov Switching GARCH Model," Asia-Pacific Financial Markets, Springer, vol. 18(1), pages 55-68, March.

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