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FORECASTING GAINS BY USING EXTREME VALUE THEORY WITH REALISED GARCH FILTER

Value-at-risk (VaR) and expected shortfall (ES) are measures of market risk that have wide applications in portfolio management, risk-adjusted performance evaluation, and computation of regulatory risk capital for financial institutions. Estimation of volatility is an integrated part of computing these measures. Although GARCH type model has been widely used traditionally to estimate this volatility, the realised GARCH model has been evolved recently as a superior variant which incorporates the information in intraday returns to provide a far more precise estimate of the underlying volatility.

In this study, we implement a novel approach of using the two-stage conditional extreme value theory (EVT) with a realised GARCH filter to generate one-step-ahead VaR and ES forecasts of the benchmark Indian equity index, S&P CNX NIFTY. We use five realised volatility measures, the 5-minute realised volatility (RV) measure, the 5-minute realised volatility measure with 1-minute subsampling (SRV), the 5-minute realised bipower variance estimator (BV), the 5-minute realised bipower variance estimator with 1-minute subsampling(SBV) and the realised kernel estimator(RK) based on tick-by-tick sampling within realised GARCH specification. Overall, we employ fourteen forecasting models, including seven standalone GARCH models and seven two stage GARCH-EVT, models to forecast VaR and ES. 

We find that the GARCH-EVT models provide significantly better quantile forecasts than the corresponding standalone GARCH models. Among the standalone GARCH models, the intraday return based realised GARCH model provides marginally better forecasting performance than GARCH and EGARCH specifications. Nonetheless, even daily return based GARCH models provide more accurate forecasts in the two stage GARCH-EVT specification than the standalone realised GARCH model. In general, the realised-GARCH EVT models provide the best forecasting performance. This finding is robust to the choice of the realised volatility estimator used to estimate the realised GARCH model. We believe such insights have important implications for practitioners and regulators.