Drawdown Risk Beyond Brownian Motion: A Monte-Carlo Framework, Non-Gaussian Extensions, and Long Memory

Battle Count: 78

The paper is directly and immediately relevant to quantitative trading. It addresses the core operational question every systematic strategy manager faces: when is a drawdown normal statistical pain versus evidence of edge decay? It provides actionable lookup tables (Tables 1, 8) for keep-or-kill decisions, quantifies how different strategy styles (trend, mean-reversion, market-neutral) distort drawdown risk relative to the Gaussian benchmark, and reveals that the √T annualisation convention can catastrophically understate multi-year risk under persistence. The practical calibration recipe (Section 7) is designed for direct implementation by risk managers.

The core Monte-Carlo simulation of drifted Brownian motion is straightforward. The GARCH(1,1) + AR(1) + NIG innovations model adds moderate complexity but uses standard algorithms. The Davies-Harte circulant-embedding method for exact fBm simulation is well-documented and vectorisable. The main implementation challenges are: (1) ensuring process-level (not path-level) normalisation to avoid Brownian bridge bias, (2) correctly implementing the horizon-fixed vs one-day-fixed normalisation for fBm, and (3) generating sufficient paths (16,000-20,000) for stable quantile estimates. No ML training or complex optimisation is required.

The paper explicitly states all figures and tables are reproducible. Fixed random seeds are used, common random numbers across Sharpe grid for smooth comparisons, 16,000-20,000 Monte-Carlo paths per cell, and a practical calibration recipe (Section 7) is provided. The Davies-Harte method for fBm simulation is a standard exact algorithm. Lookup tables are provided for direct use. The author acknowledges AI-assisted tools for coding/validation but takes full responsibility for modelling choices.