Limiting Distribution of the Maximum Drawdown for Brownian Motion with Positive Drift

Hans-Peter Bermin () and Magnus Holm ()
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Hans-Peter Bermin: Affiliated with Lund University, Knut Wicksell Centre for Financial Studies, Postal: School of Economics and Management, Box 7080, S-220 07 Lund, Sweden
Magnus Holm: Hilbert Group AB, Postal: 171 Old Bakery Street, , VLT 1455, , Malta

No 2025:9, Working Papers from Lund University, Department of Economics

Abstract: The maximum drawdown of a stochastic process is the largest peak-to-trough decline observed over a given horizon. Using arguments from extreme value theory, we derive the limiting distribution of the maximum drawdown for a Brownian motion with positive drift. We show that, after suitable centering and scaling, the maximum drawdown converges in distribution to the Gumbel law.

Keywords: maximum drawdown; extreme value theory; asymptotic distribution (search for similar items in EconPapers)
JEL-codes: G11 G32 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2025-11-13
New Economics Papers: this item is included in nep-rmg
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