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Hedging options in a hidden Markov‐switching local‐volatility model via stochastic flows and a Monte‐Carlo method

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  • Robert J. Elliott
  • Tak Kuen Siu

Abstract

The hedging of European contingent claims in a continuous‐time hidden Markov‐regime‐switching diffusion model is discussed using stochastic flows of diffeomorphisms and Monte‐Carlo simulations. Specifically, the price dynamics of an underlying risky asset are governed by a continuous‐time hidden Markov‐modulated local‐volatility model. Filtering theory is used to estimate the unobservable drift given observable price information and to define a filtered market with complete observations. The delta–hedge ratio of a European option is derived using a martingale representation and stochastic flows of diffeomorphisms. The numerical computation of the delta–hedge ratio is estimated via Monte‐Carlo simulations. Numerical results for illustrating the proposed method and the (relative) importance of the impacts of the information risk and the local‐volatility parametrizations on the delta–hedge ratio are provided for the case of European call options.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:43:y:2023:i:7:p:925-950
    DOI: 10.1002/fut.22422
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    References listed on IDEAS

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    1. Merton, Robert C., 1977. "On the pricing of contingent claims and the Modigliani-Miller theorem," Journal of Financial Economics, Elsevier, vol. 5(2), pages 241-249, November.
    2. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
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    5. 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.
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