Drawdown and Drawup for Fractional Brownian Motion with Trend

Long Bai; Peng Liu

doi:10.1007/s10959-018-0836-y

Drawdown and Drawup for Fractional Brownian Motion with Trend

Long Bai, Peng Liu^*

^*Corresponding author for this work

University of Lausanne

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1581-1612
Number of pages	32
Journal	Journal of Theoretical Probability
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s10959-018-0836-y
Publication status	Published - 1 Sept 2019
Externally published	Yes

Keywords

Drawdown
Drawup
Fractional Brownian motion
Geometric fractional Brownian motion
Pickands constant
Piterbarg constant

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10.1007/s10959-018-0836-y

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AB - 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.

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KW - Drawup

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KW - Geometric fractional Brownian motion

KW - Pickands constant

KW - Piterbarg constant

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Drawdown and Drawup for Fractional Brownian Motion with Trend

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Keywords

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