Drawdown and drawup for fractional Brownian motion with trend

Long Bai; Peng Liu

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arXiv · 1801.10598

Drawdown and drawup for fractional Brownian motion with trend

Long Bai·Peng Liu

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Abstract

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

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Long Bai, Peng Liu. 2018-01-31. Drawdown and drawup for fractional Brownian motion with trend. https://arxiv.org/abs/1801.10598

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