A conditional extreme value volatility estimator based on high-frequency returns

Abstract

This paper introduces a conditional extreme value volatility estimator (EVT) based on high-frequency returns. The relative performance of the EVT is compared with the discrete-time GARCH and implied volatility models for 1-day and 20-day-ahead forecasts of realized volatility. This is also a first attempt towards detecting any time-series variation in extreme value distributions using high-frequency intraday data. The information content of EVT is examined in the context of forecasting S&P 100 index volatility. Adjusted- R 2 values imply superior performance of the implied volatility index (VIX) and EVT in capturing time-series variation in realized volatility. The forecasting ability of various discrete-time GARCH models turns out to be inferior to VIX and EVT. According to the Theil inequality coefficient and the heteroscedasticity-adjusted root mean squared and mean absolute errors, (1) EVT provides more accurate forecasts than the VIX and GARCH volatility models; (2) VIX generally yields a less accurate characterization of realized volatility than EVT and GARCH models. These results have implications for financial risk management, and are thus relevant to both regulators and practitioners.