2T-POT Hawkes model for left- and right-tail conditional quantile forecasts of financial log returns: Out-of-sample comparison of conditional EVT models

Conditional extreme value theory (EVT) methods promise enhanced forecasting of the extreme tail events that often dominate systemic risk. We present an improved two -tailed peaks-over-threshold (2T-POT) Hawkes model that is adapted for conditional quantile forecasting in both the left and right tails of a univariate time series. This is applied to the daily log returns of six large-cap indices. We also take the unique step of fitting the model at multiple exceedance thresholds (from the 1.25% to 25.00% mirrored quantiles). Quantitatively similar asymmetries in Hawkes parameters are found across all six indices, adding further empirical support to a temporal leverage effect in financial price time series in which the impact of losses is not only larger but also more immediate. Out-of-sample backtests find that our 2T-POT Hawkes model is more reliably accurate than the GARCH-EVT model when forecasting (mirrored) value at risk and expected shortfall at the 5% coverage level and below. This suggests that asymmetric Hawkes-type arrival dynamics are a better approximation of the true generating process for extreme daily log returns than GARCH-type conditional volatility. Our 2T -POT Hawkes model therefore presents a better-performing alternative for financial risk modelling.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of International Institute of Forecasters. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study presents an improved two-tailed extreme value model that is adapted for quantile forecasting in both the left and right tails of financial time series. Results show similar asymmetries in the model parameters across multiple indices, supporting the temporal leverage effect in financial price time series. Out-of-sample testing demonstrates that the proposed model outperforms the traditional GARCH-EVT model in forecasting value at risk and expected shortfall.