Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2025:9: Limiting Distribution of the Maximum Drawdown for Brownian Motion with Positive Drift

Hans-Peter Bermin () and Magnus Holm ()
Additional contact information
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

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

JEL-codes: G11; G32

Language: English

18 pages, November 13, 2025

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