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.

Additional Metadata
Keywords forecasting, realized volatility, value-at-risk, volatility of volatility
JEL Semiparametric and Nonparametric Methods (jel C14), Time-Series Models; Dynamic Quantile Regressions (jel C22), Econometric Modeling: General (jel C50), International Financial Markets (jel G15)
Publisher Tinbergen Institute
Persistent URL hdl.handle.net/1765/40960
Series Tinbergen Institute Discussion Paper Series
Journal Discussion paper / Tinbergen Institute
Citation
Allen, D.E, McAleer, M.J, & Scharth, M. (2013). Realized Volatility Risk (No. TI 13-092/III). Discussion paper / Tinbergen Institute (pp. 1–34). Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/40960