Stock index Value-at-Risk forecasting: A realized volatility extreme value theory approach

In this study, we propose the use of Heterogeneous Autoregressive (HAR) type realized volatility models in combination with the Extreme Value Theory (EVT) method for Value-at-Risk (VaR) forecasting. The proposed model accounts for the long memory property of the realized volatility and the fat tails of the returns distribution. The out-of-sample forecasting results, based on the S&P 500 stock index, indicate that the HAR-type-EVT models outperform their GARCH-type counterparts in terms of statistical and regulatory accuracy as well as capital efficiency. The HAR-GARCH-EVT model, which also accounts for the conditional heteroscedasticity of the HAR errors, is the overall best performing model as it generates accurate VaR estimates that minimize the Basel II regulatory capital during both the full out-of-sample period and the 2007-2009 crisis period.