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Drawdown and Drawup for Fractional Brownian Motion with Trend

Author

Listed:
  • Long Bai

    (University of Lausanne, UNIL-Dorigny)

  • Peng Liu

    (University of Lausanne, UNIL-Dorigny)

Abstract

We consider the drawdown and drawup of a fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in a financial market. We derive the asymptotics of tail probabilities of the maximum drawdown and maximum drawup, respectively, as the threshold goes to infinity. It turns out that the extremes of drawdown lead to new scenarios of asymptotics depending on the Hurst index of fractional Brownian motion.

Suggested Citation

  • Long Bai & Peng Liu, 2019. "Drawdown and Drawup for Fractional Brownian Motion with Trend," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1581-1612, September.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0836-y
    DOI: 10.1007/s10959-018-0836-y
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    References listed on IDEAS

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    Cited by:

    1. Tommaso Proietti, 2024. "Ups and (Draw)Downs," CEIS Research Paper 576, Tor Vergata University, CEIS, revised 03 May 2024.

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