Volatility is the primary measure of risk in modern finance and volatility estimation and inference has attracted substantial attention in the recent financial econometric literature, especially in high-frequency analyses. High-frequency prices carry a significant amount of noise. Therefore, there are two volatility components embedded in the returns constructed using high frequency prices: the...

F orecasting the volatility of a financial asset has wide implications in finance. Conditional variance extracted from the GARCH framework could be a suitable proxy of financial asset volatility. Option pricing, portfolio optimization, and risk management are examples of implications of conditional variance forecasting. One of the most recent methods of volatility forecasting is Real...

We forecast realized volatility extending the heterogeneous autoregressive model (HAR) to include implied (IV), leverage effect, overnight returns, and of volatility. analyze 10 international stock indices finding that, although a simple HAR augmented with IV (HAR-IV) is more accurate than any excluding it, all markets support further extensions HAR-IV model. More forecasts are found using retu...

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...