Regularized Extreme Value Regression for High-Frequency Tail Risk

Summary

The study models how the severity of extreme losses in high-frequency markets changes with trading activity and market uncertainty. Its dynamic extreme value regression accommodates both stationary and local unit-root predictors, addressing predictor behavior that may otherwise distort estimates of changing tail risk. Candidate predictors include measures of volatility and liquidity.

To choose relevant predictors, the authors propose a two-step adaptive L1-regularized maximum likelihood estimator. They establish an oracle property for selecting both predictor types and report favorable finite-sample behavior in simulations. An empirical study of high-frequency extreme losses in nine liquid U.S. stocks uses 42 liquidity and volatility measures; it finds that loss severity is predictable in settings with low price impact and elevated volatility measures. The excerpt does not give forecast performance metrics or establish how well the results transfer to other assets, markets, or trading settings.

Key ideas

• The model links high-frequency extreme loss severity to liquidity and volatility predictors.
• It allows predictors to be stationary or locally unit-root processes.
• An adaptive L1-regularized likelihood method selects predictors.
• The study reports theoretical selection properties and supportive simulation results.
• In the stock sample, low price impact alongside high volatility measures helps predict extreme loss severity.

Tags

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


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









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.

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