Drawdowns preceding rallies in the Brownian motion model

Olympia Hadjiliadis and Jan Vecer

Quantitative Finance, 2006, vol. 6, issue 5, 403-409

Abstract: We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market crashes and rallies in the geometric Brownian motion model.

Keywords: Drawdowns; Brownian motion model; Rallies (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (20)

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DOI: 10.1080/14697680600764227

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