In this paper, we document that realized variation measures constructed from high-frequency 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 unpredict...

We will in some places restrict attention to puts, by put-call parity: for realized variance options, a long-call short-put combination pays [X]T −Q, equal to a Q-strike variance swap; and for realized volatility options, a long-call short-put combination pays [X] T − Q1/2, equal to a Q1/2-strike volatility swap. Unlike variance swaps [EQF07/024, EQF07/045], which admit exact model-free (assumi...

We decompose volatility of a stock market index both in time and scale using wavelet filters and design a probabilistic indicator for volatilities, analogous to the Richter scale in geophysics. The peakover-threshold method is used to fit the generalized Pareto probability distribution for the extreme values in the realized variances of wavelet coefficients. The indicator is computed for the da...