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Drawdown and Drawup for Fractional Brownian Motion with Trend

Drawdown and Drawup for Fractional Brownian Motion with Trend 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Theoretical Probability Springer Journals

Drawdown and Drawup for Fractional Brownian Motion with Trend

Bai, Long; Liu, Peng
Journal of Theoretical Probability , Volume 32 (3) – Jun 6, 2018
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32 pages

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Probability Theory and Stochastic Processes; Statistics, general
ISSN
0894-9840
eISSN
1572-9230
DOI
10.1007/s10959-018-0836-y
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Theoretical Probability – Springer Journals

Published: Jun 6, 2018

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