Using estimators of the variation of positive and negative returns (realized semivariances) and high-frequency data for the S&P 500 Index and 105 individual stocks, this paper sheds new light on the predictability of equity price volatility.We showthat future volatility is more strongly related to the volatility of past negative returns than to that of positive returns and that the impact of a price jump on volatility depends on the sign of the jump, with negative (positive) jumps leading to higher (lower) future volatility. We show that models exploiting these findings lead to significantly better out-of-sample forecast performance.

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Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility

SUMMARY
We introduce a new framework, Realized GARCH, for the joint modeling of returns and realized measures of volatility. A key feature is a measurement equation that relates the realized measure to the conditional variance of returns. The measurement equation facilitates a simple modeling of the dependence between returns and future volatility. Realized GARCH models with a linear or log-linear specification have many attractive features. They are parsimonious, simple to estimate, and imply an ARMA structure for the conditional variance and the realized measure. An empirical application with Dow Jones Industrial Average stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads to substantial improvements in the empirical fit over standard GARCH models that only use daily returns. Copyright © 2011 John Wiley & Sons, Ltd.

http://public.econ.duke.edu/~get/browse/courses/201/spr12/DOWNLOADS/WorkingPapers_Now_Published/phs_realized_garch_10.pdf

Realized GARCH: a joint model for returns and realized measures of volatility

https://hal.archives-ouvertes.fr/hal-00815564/document

Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

This paper studies in some detail a class of high-frequency-based volatility (HEAVY) models These models are direct models of daily asset return volatility based on realised measures constructed from high-frequency data Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models We analyse a model-based bootstrap which allows us to estimate the entire predictive distribution of returns We also provide an analysis of missing data in the context of these models Copyright © 2010 John Wiley & Sons, Ltd

/pdf/realising-the-future-forecasting-with-high-frequency-based-4svz53w4gj.pdf

Realising the future: forecasting with high‐frequency‐based volatility (HEAVY) models

https://www.nber.org/system/files/working_papers/w15533/w15533.pdf

Jump-Robust Volatility Estimation using Nearest Neighbor Truncation

Summary Realized kernels use high-frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same stock and find a remarkable level of agreement.



We identify some features of the high-frequency data, which are challenging for realized kernels. They are when there are local trends in the data, over periods of around 10 minutes, where the prices and quotes are driven up or down. These can be associated with high volumes. One explanation for this is that they are due to non-trivial liquidity effects.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1368-423X.2008.00275.x

P. Reinhard Hansen

Papers

Realized kernels in practice: trades and quotes