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A Dupire Equation For A Regime-Switching Model

Author

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  • ROBERT J. ELLIOTT

    (School of Mathematical Sciences, The University of Adelaide, Adelaide 5005, Australia;
    Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada;
    Centre for Applied Financial Studies, University of South Australia, Adelaide, Australia)

  • LEUNGLUNG CHAN

    (School of Mathematics and Statistics, University of New South Wales, NSW 2052, Australia)

  • TAK KUEN SIU

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

Abstract

A forward equation, which is also called the Dupire formula, is obtained for European call options when the price dynamics of the underlying risky assets are assumed to follow a regime-switching local volatility model. Using a regime-switching version of the adjoint formula, a system of coupled forward equations is derived for the price of the European call over different states of the economy.

Suggested Citation

  • Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2015. "A Dupire Equation For A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-13.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:04:n:s0219024915500235
    DOI: 10.1142/S0219024915500235
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    References listed on IDEAS

    as
    1. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
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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.
    2. Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    3. Zhang, Ziqing, 2024. "Multi-regime foreign exchange rate model: Calibration and pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 204-218.
    4. Xin-Jiang He & Song-Ping Zhu, 2019. "Variance And Volatility Swaps Under A Two-Factor Stochastic Volatility Model With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-19, June.
    5. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    6. Xin‐Jiang He & Song‐Ping Zhu, 2018. "On full calibration of hybrid local volatility and regime‐switching models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(5), pages 586-606, May.
    7. Xin‐Jiang He & Sha Lin, 2023. "Analytically pricing European options under a hybrid stochastic volatility and interest rate model with a general correlation structure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 951-967, July.

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