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Attainable Contingent Claims In A Markovian Regime-Switching Market

Author

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  • ROBERT J. ELLIOTT

    (School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia;
    Haskayne School of Business, University of Calgary, Calgary, Canada)

  • TAK KUEN SIU

    (Cass Business School, City University, 106 Bunhill Row, London EC1Y 8TZ, UK;
    Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia)

Abstract

It is known that the market in a Markovian regime-switching model is, in general, incomplete, so not all contingent claims can be perfectly hedged. We show, in this paper, how certain contingent claims are attainable in the regime-switching market using a money market account, a share and a zero-coupon bond. General contingent claims with payoffs depending on both the share price and the state of the regime-switching process are considered. We apply a martingale representation result to show the attainability of a European-style contingent claim. We also extend our analysis to Asian-style and American-style contingent claims.

Suggested Citation

  • Robert J. Elliott & Tak Kuen Siu, 2012. "Attainable Contingent Claims In A Markovian Regime-Switching Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-19.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:n:s0219024912500550
    DOI: 10.1142/S0219024912500550
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    Cited by:

    1. Robert J. Elliott & Tak Kuen Siu, 2023. "Hedging options in a hidden Markov‐switching local‐volatility model via stochastic flows and a Monte‐Carlo method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 925-950, July.

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