Forecasting tail risk measures for financial time series: an extreme value approach with covariates

Abstract

The paper develops a tail risk forecasting model that incorporates the wealth of economic and financial information available to risk managers. The approach can be viewed as a regularized extension of the two-stage GARCH-EVT model of McNeil and Frey (2000) where we permit a time-varying data-driven selection of a sparse set of covariates affecting the scale of the extreme value distribution of risk. We use a rich data set from the U.S. equity market to explore when this additional information improves Value-at-Risk and Expected Shortfall forecasts compared to popular tail risk forecasting methods such as the traditional and non-regularized GARCH-EVT models, and the GJR-GARCH(1,1), Hawkes POT model, CaViaR and CARE models. Under an extensive set of performance criteria and tests we demonstrate that our approach produces competitive risk forecasts, particularly during periods of financial distress.