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When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

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  • Xin Guo

    (IBM T. J. Watson Research Center)

Abstract

Let Θt be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when Θt is in different states. This new process Zt is a hidden Markov process. We study the probability distribution of the first passage time for Zt. Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).

Suggested Citation

  • Xin Guo, 2001. "When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process," Methodology and Computing in Applied Probability, Springer, vol. 3(2), pages 135-143, June.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:2:d:10.1023_a:1012201109468
    DOI: 10.1023/A:1012201109468
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    References listed on IDEAS

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    1. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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