Volatility measures and Value-at-Risk

Abstract

We evaluate and compare the abilities of the implied volatility and historical volatility models to provide accurate Value-at-Risk forecasts. Our empirical tests on the S&P 500, Dow Jones Industrial Average and Nasdaq 100 indices over long time series of more than 20 years of daily data indicate that an implied volatility based Value-at-Risk cannot beat, and tends to be outperformed by, a simple GJR-GARCH based Value-at-Risk. This finding is robust to the use of the likelihood ratio, the dynamic quantile test or a statistical loss function for evaluating the Value-at-Risk performance.The poor performance of the option based Value-at-Risk is due to the volatility risk premium embedded in implied volatilities. We apply both non-parametric and parametric adjustments to correct for the negative price of the volatility risk. However, although this adjustment is effective in reducing the bias, it still does not allow the implied volatility to outperform the historical volatility models.These results are in contrast to the volatility forecasting literature, which favors implied volatilities over the historical volatility model. We show that forecasting the volatility and forecasting a quantile of the return distribution are two different objectives. While the implied volatility is useful for the earlier objective function, it is not for the latter, due to the non-linear and regime changing dynamics of the volatility risk premium.