Option pricing for GARCH models with Markov switching

Robert J. Elliott, Tak Kuen Siu, Leunglung Chan

Research output: Contribution to journalArticle

13 Citations (Scopus)

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. © World Scientific Publishing Company.

Original languageEnglish
Pages (from-to)825-841
Number of pages17
JournalInternational Journal of Theoretical and Applied Finance
Volume9
Issue number6
DOIs
Publication statusPublished - Sep 2006

Keywords

  • Analytical option valuation
  • Markov switching conditional Esscher transform
  • Markov switching Heston-Nandi's GARCH model
  • Recursive formula

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