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Option pricing under regime switching

Author

Listed:
  • Jin-Chuan Duan
  • Ivilina Popova
  • Peter Ritchken

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.

Suggested Citation

  • Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
  • Handle: RePEc:taf:quantf:v:2:y:2002:i:2:p:116-132
    DOI: 10.1088/1469-7688/2/2/303
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    Citations

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    Cited by:

    1. Ma, Jingtang & Li, Wenyuan & Han, Xu, 2015. "Stochastic lattice models for valuation of volatility options," Economic Modelling, Elsevier, vol. 47(C), pages 93-104.
    2. Jin-Chuan Duan & Peter H. 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.
    3. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    4. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    5. repec:eee:apmaco:v:251:y:2015:i:c:p:453-468 is not listed on IDEAS
    6. 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.
    7. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    8. En-Der Su & Feng-Jeng Lin, 2012. "Two-State Volatility Transition Pricing and Hedging of TXO Options," Computational Economics, Springer;Society for Computational Economics, vol. 39(3), pages 259-287, March.
    9. Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    10. Chourdakis, Kyriakos & Dendramis, Yiannis & Tzavalis, Elias, 2014. "Are regime-shift sources of risk priced in the market?," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 151-170.
    11. Massimo Guidolin, 2013. "Markov switching models in asset pricing research," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 1, pages 3-44 Edward Elgar Publishing.
    12. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    13. repec:spr:annopr:v:257:y:2017:i:1:d:10.1007_s10479-015-1887-4 is not listed on IDEAS
    14. repec:spr:annopr:v:237:y:2016:i:1:d:10.1007_s10479-014-1651-1 is not listed on IDEAS
    15. Julia Eisenberg & Paul Kruhner, 2016. "The Impact of Negative Interest Rates on Optimal Capital Injections," Papers 1612.06654, arXiv.org.
    16. Lian, Yu-Min & Liao, Szu-Lang & Chen, Jun-Home, 2015. "State-dependent jump risks for American gold futures option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 115-133.
    17. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    18. Hiroshi Ishijima & Masaki Uchida, 2011. "Log Mean-Variance Portfolio Selection Under Regime Switching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(2), pages 213-229, May.
    19. Vanden, Joel M., 2005. "Equilibrium analysis of volatility clustering," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 374-417, June.
    20. Pascal François & Geneviève Gauthier & Frédéric Godin, 2012. "Optimal Hedging when the Underlying Asset Follows a Regime-switching Markov Process," Cahiers de recherche 1234, CIRPEE.

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