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A Hidden Markov-Modulated Jump Diffusion Model for European Option Pricing

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Hidden Markov Models in Finance

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 209))

Abstract

The valuation of a European-style contingent claim is discussed in a hidden Markov regime-switching jump-diffusion market, where the evolution of a hidden economic state process over time is described by a continuous-time, finite-state, hidden Markov chain. A two-stage procedure is used to discuss the option valuation problem. Firstly filtering theory is employed to transform the original market with hidden quantities into a filtered market with complete observations. Then a generalized version of the Esscher transform based on a Doléan-Dade stochastic exponential is employed to select a pricing kernel in the filtered market. A partial-differential-integral equation for the price of a European-style option is presented.

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Author information

Authors and Affiliations

  1. Cass Business School, City University London, 106 Bunhill Row, EC1Y 8TZ, London, UK

    Tak Kuen Siu

  2. Faculty of Business and Economics, Department of Applied Finance and Actuarial Studies, Macquarie University, Sydney, NSW, 2109, Australia

    Tak Kuen Siu

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  1. Tak Kuen Siu
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Correspondence to Tak Kuen Siu .

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Editors and Affiliations

  1. Dept of Statistical & Actuarial Sciences, University of Western Ontario, London, Ontario, Canada

    Rogemar S. Mamon

  2. School of Mathematics, University of Adelaide, Adelaide, Australia

    Robert J. Elliott

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Siu, T.K. (2014). A Hidden Markov-Modulated Jump Diffusion Model for European Option Pricing. In: Mamon, R., Elliott, R. (eds) Hidden Markov Models in Finance. International Series in Operations Research & Management Science, vol 209. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7442-6_8

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