Realized quantity extended conditional autoregressive value-at-risk models

This paper introduces quantile models that incorporate realized variance, realized semivariance, jump variation and jump semivariation based on a conditional autoregressive quantile regression model framework for improved value-at-risk (VaR) and improved joint forecasts of VaR and expected shortfall (ES), which we denote by .VaR; ES/. Our empirical results show that high-frequency-data-based realized quantities lead to better VaR and .VaR; ES/ forecasts. We evaluate these using conditional coverage and dynamic quantile backtests for VaR, regression-based backtests for .VaR; ES/ and comparison tests based on scoring functions and model confidence sets. The study includes data sets covering the global financial crisis of 2007–9 and the Covid-19 pandemic to ensure stability over different market conditions. The results indicate that realized quantity extensions improve forecasts in terms of classic and comparison tests for all quantile levels and time periods, with stand-alone VaR forecasts benefiting the most. It is shown that the symmetric absolute value quantile model benefits the most from realized semivariance extension, whereas the asymmetric slope model benefits the most from realized variance extension.