Realized volatility uncertainty

The presence of high and time-varying volatility of volatility and leverage effects bring additional uncertainty in the tails of the distribution of asset returns, even though returns standardized by (ex-post) quadratic variation measures are nearly gaussian. We argue that in this setting modeling shocks to volatility is more relevant for applications than extracting more precise predictions of the variable, as point forecasts differences are swamped by the size of the volatility of volatility and rendered less informative by the nongaussianity in the ex-ante distribution of returns. Using S&P 500 data, we document that this volatility of volatility is subject to strong leverage effects, short-lived explosive regimes and is strongly and positively related to the level of volatility. Starting from a mixing hypothesis for volatility and returns, we propose a Monte Carlo method for translating these features into refined density forecasts for returns from our conditional volatility, skewness and kurtosis framework. We show how this method brings large improvements over traditional approaches for density and risk forecasting