Lévy-stable scaling of risk and performance functionals

Battle Count: 77

Highly relevant to quantitative trading. The paper directly addresses the core risk and performance metrics (VaR, ES, Sharpe, IR, Kelly, drawdown) used daily by quantitative traders and risk managers. It provides explicit corrections to the ubiquitous √τ Gaussian scaling that systematically misprices tail risk on heavy-tailed liquid assets. The horizon-correct formulas are immediately applicable to position sizing, capital allocation, backtesting, and regulatory compliance. The nonparametric nature (requiring only α and tail quantiles) makes it practical for implementation in trading systems.

Moderate complexity. The theoretical framework is elegant with closed-form solutions, but practical implementation requires: (1) computing α-stable distribution quantiles numerically (using Nolan's stable package or similar), (2) estimating the tail index α via central-mass regression, (3) identifying window edges via two-segment scale fitting, (4) handling the α-mixing conditions for valid inference, and (5) choosing appropriate anchor horizons and tail quantiles. The formulas themselves are straightforward once α and the window are estimated, but the estimation pipeline and numerical stable-distribution computations add complexity.

The paper provides fully closed-form formulas and nonparametric estimators (central-mass slope, two-segment scale fit) that are theoretically reproducible. However, no code, data, or software implementation is provided. Reproduction requires access to high-frequency liquid-asset return data and numerical routines for α-stable quantiles (e.g., Nolan's stable distribution package). The methodology is self-contained mathematically but lacks empirical validation tables.