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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