Trapezoidal Frustum and Angle Bracket for the Maximum Drawdown
Journal
Proceedings of the IEEE International Conference on Big Data, BigData
Journal Issue
2025
Start Page
5940
End Page
5946
ISSN
25732978
ISBN (of the container)
9798331594473
Date Issued
2025-12-08
Author(s)
Syu, Jia-Hao
Abstract
Maximum drawdown (MDD) is a widely used measure in investment evaluation. In this paper, we focus on calculating AαT, the probability that the MDD is at least α during T years when the price follows a GBM, for which no closed-form formula is known. We propose an O(n2)-time trapezoidal frustum and an O(n1.5 log n)-time angle bracket to calculate AαT, where n is the number of time steps. Experiments confirm the accuracy of the proposed methods, with the angle bracket outperforming the trapezoidal frustum in terms of both convergence and efficiency.
Event(s)
2025 IEEE International Conference on Big Data, BigData 2025
Subjects
binomial tree
fast Fourier transform
maximum drawdown
reflection principle
Publisher
IEEE
Type
conference paper