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Option pricing under regime switching

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  • Jin-Chuan Duan
  • Ivilina Popova
  • Peter Ritchken
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    Abstract

    This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357-84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 2 (2002)
    Issue (Month): 2 ()
    Pages: 116-132

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    Handle: RePEc:taf:quantf:v:2:y:2002:i:2:p:116-132

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    Cited by:
    1. Hiroshi Ishijima & Masaki Uchida, 2011. "Log Mean-Variance Portfolio Selection Under Regime Switching," Asia-Pacific Financial Markets, Springer, vol. 18(2), pages 213-229, May.
    2. En-Der Su & Feng-Jeng Lin, 2012. "Two-State Volatility Transition Pricing and Hedging of TXO Options," Computational Economics, Society for Computational Economics, vol. 39(3), pages 259-287, March.
    3. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Paper 0619, Federal Reserve Bank of Cleveland.
    4. Kuang-Liang Chang & Nan-Kuang Chen & Charles Leung, 2011. "Monetary Policy, Term Structure and Asset Return: Comparing REIT, Housing and Stock," The Journal of Real Estate Finance and Economics, Springer, vol. 43(1), pages 221-257, July.
    5. Vanden, Joel M., 2005. "Equilibrium analysis of volatility clustering," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 374-417, June.
    6. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    7. Pascal François & Geneviève Gauthier & Frédéric Godin, 2012. "Optimal Hedging when the Underlying Asset Follows a Regime-switching Markov Process," Cahiers de recherche 1234, CIRPEE.
    8. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Centre de Recherche en Economie et Statistique.
    9. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.

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