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 data 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.