Drawdown and Drawup for Fractional Brownian Motion with Trend

Long Bai () and Peng Liu ()
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Long Bai: University of Lausanne, UNIL-Dorigny
Peng Liu: University of Lausanne, UNIL-Dorigny

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1581-1612

Abstract: 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.

Keywords: Drawdown; Drawup; Fractional Brownian motion; Geometric fractional Brownian motion; Pickands constant; Piterbarg constant; Primary 60G15; Secondary 60G70 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-018-0836-y

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