Measuring tail risk at high-frequency: An $L_1$-regularized extreme value regression approach with unit-root predictors

Paper: arXiv 2301.01362

Authors: Julien Hambuckers, Li Sun, Luca Trapin

Abstract

We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root predictors to appropriately capture the time-varying behaviour of the distribution of high-frequency extreme losses. To characterize trading activity and market uncertainty, we consider several volatility and liquidity predictors, and propose a two-step adaptive $L_1$-regularized maximum likelihood estimator to select the most appropriate ones. We establish the oracle property of the proposed estimator for selecting both stationary and local unit-root predictors, and show its good finite sample properties in an extensive simulation study. Studying the high-frequency extreme losses of nine large liquid U.S. stocks using 42 liquidity and volatility predictors, we find the severity of extreme losses to be well predicted by low levels of price impact in period of high volatility of liquidity and volatility.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated extreme value regression model, complete with theoretical proofs like the oracle property for local unit-root predictors. It complements this rigorous theory with an extensive empirical application evaluating 42 high-frequency market predictors across major U.S. equities.

Research Flowchart

  flowchart TD
    A[Goal: Predict High-Frequency Tail Risk & Identify Key Predictors] --> B[Input Data: High-frequency trade data for 9 US stocks & 42 volatility/liquidity predictors]
    B --> C[Model: Dynamic Extreme Value Regression with Stationary & Unit-Root Predictors]
    C --> D[Methodology: Two-Step Adaptive L1-Regularized Maximum Likelihood Estimation]
    D --> E[Validation: Asymptotic Oracle Property Proof & Finite Sample Simulations]
    E --> F[Outcomes: Model selects key predictors; reveals extreme losses are driven by low price impact during high liquidity/volatility swings]