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...

For a given time horizon ∆T , this article explores the relationship between the realized volatility (the volatility that will occur between t and t + ∆T ), the implied volatility (corresponding to at-the-money option with expiry at t+∆T ), and several forecasts for the volatility build from multi-scales linear ARCH processes. The forecasts are derived from the process equations, and the parame...

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...

The paper studies the nonparametric connection between realized and implied volatilities. No-arbitrage identities and comparison inequalities are found. We formulate the multi-factor trading system on the volatility scale. To empirically determine the number of factors, we develop a high frequency analysis for sequential F-testing. We also design a cross validated estimate of quadratic variation.

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...