This discussion paper led to an article in the Journal of Risk and Financial Management (2014). Volume 7(2), pages 80-109.
In this paper we document that realized variation measures constructed from highfrequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Explicitly modeling this volatility risk is fundamental.
We propose a dually asymmetric realized volatility model, which incorporates the fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed
account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.