Early empirical evidence suggests that the realised generalised autoregressive conditional heteroskedasticity (GARCH) model provides significant forecasting gains over the standard GARCH models in volatility forecasting. We extend this literature in quantile forecasting by implementing conditional extreme value theory (EVT) framework with realised GARCH. We generate one-step-ahead value-at-risk (VaR) and expected shortfall (ES) forecasts for the S&P CNX NIFTY index using 14 standalone GARCH and GARCH-EVT models. In out-of-sample comparisons, the GARCH-EVT specification generally outperforms the standalone GARCH models. In general, the realised-GARCH EVT models provide the best forecasting performance. This finding is robust to the choice of different realised volatility estimators used to estimate realised GARCH.

早期的经验证据表明，与标准 GARCH 模型相比，已实现的广义自回归条件异方差 (GARCH) 模型在波动率预测中提供了显着的预测收益。我们通过使用已实现的 GARCH 实施条件极值理论 (EVT) 框架，在分位数预测中扩展了这些文献。我们使用 14 个独立的 GARCH 和 GARCH-EVT 模型为 S&P CNX NIFTY 指数生成提前一步的风险价值 (VaR) 和预期缺口 (ES) 预测。在样本外比较中，GARCH-EVT 规范通常优于独立的 GARCH 模型。总的来说，realised-GARCH EVT 模型提供了最好的预测性能。这一发现对于用于估计已实现 GARCH 的不同已实现波动率估算器的选择是稳健的。