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

TL;DR

This paper develops a novel $L_1$-regularized extreme value regression model to analyze and predict tail risk dynamics in high-frequency financial markets, incorporating both stationary and local unit-root predictors.

Contribution

It introduces a new adaptive $L_1$-regularized estimator with proven oracle properties for selecting relevant predictors in tail risk modeling.

Findings

Extreme losses are predicted by low price impact during high volatility periods.

The proposed model accurately captures the time-varying behavior of high-frequency tail risks.

Simulation results demonstrate the estimator's good finite sample performance.

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.