A Reduced Form Framework for Modeling Volatility of Speculative Prices Based on Realized Variation Measures

Journal of Econometrics, Vol. 160, Issue 1, pp. 176-189, January 2011

CREATES Research Paper 2007-14

31 Pages Posted: 23 Jun 2008 Last revised: 7 Jan 2012

See all articles by Torben G. Andersen

Torben G. Andersen

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Aarhus University - CREATES

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Xin Huang

Board of Governors of the Federal Reserve System

Date Written: May 15, 2008

Abstract

Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability is well described by an approximate long-memory HAR-GARCH model, while the overnight returns may be modelled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Lastly, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.

Keywords: Stochastic Volatility, Realized Variation, Bipower Variation, Jumps, Hazard Rates, Overnight Volatility

JEL Classification: C1, G1, C2

Suggested Citation

Andersen, Torben G. and Bollerslev, Tim and Huang, Xin, A Reduced Form Framework for Modeling Volatility of Speculative Prices Based on Realized Variation Measures (May 15, 2008). Journal of Econometrics, Vol. 160, Issue 1, pp. 176-189, January 2011; CREATES Research Paper 2007-14. Available at SSRN: https://ssrn.com/abstract=1150050 or http://dx.doi.org/10.2139/ssrn.1150050

Torben G. Andersen (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
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Aarhus University - CREATES ( email )

School of Economics and Management
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DK-8000 Aarhus C
Denmark

Tim Bollerslev

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Xin Huang

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

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