Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns

CREATES Research Paper No. 2007-21

74 Pages Posted: 23 Jun 2008 Last revised: 2 Dec 2008

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)

Per Skaarup Frederiksen

BlackRock, Inc

Morten Ørregaard Nielsen

Queen's University - Department of Economics

Margit Sommer

School of Economics and Management, University of Aarhus; School of Economics and Management; CREATES Research Papers

Date Written: August 13, 2007

Abstract

We provide an empirical framework for assessing the distributional properties of daily speculative returns within the context of the continuous-time modeling paradigm traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non-parametric jump detection statistics constructed from high-frequency intraday data. A sequence of relatively simple-to-implement moment-based tests involving various transforms of the daily returns speak directly to the import of different features of the underlying continuous-time processes that might have generated the data. As such, the tests may serve as a useful diagnostic tool in the specification of empirically more realistic asset pricing models. Our results are also directly related to the popular mixture-of-distributions hypothesis and the role of the corresponding latent information arrival process. On applying our sequential test procedure to the thirty individual stocks in the Dow Jones Industrial Average index, the data suggest that it is important to allow for both time-varying diffusive volatility, jumps, and leverage effects in order to satisfactorily describe the daily stock price dynamics. At a broader level, the empirical results also illustrate how the realized variation measures and high-frequency sampling schemes may be used in eliciting important distributional features and asset pricing implications more generally.

Keywords: Return distributions, continuous-time models, mixture-of-distributions hypothesis, financial-time sampling, high-frequency data, volatility signature plots, realized volatilities, jumps, leverage and volatility feedback effects

JEL Classification: C1, G1

Suggested Citation

Andersen, Torben G. and Bollerslev, Tim and Frederiksen, Per Skaarup and Nielsen, Morten Orregaard and Sommer, Margit, Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns (August 13, 2007). CREATES Research Paper No. 2007-21. Available at SSRN: https://ssrn.com/abstract=1150086 or http://dx.doi.org/10.2139/ssrn.1150086

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
United States

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
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

Per Skaarup Frederiksen

BlackRock, Inc ( email )

55 East 52nd Street
New York City, NY 10055
United States
+4529729092 (Phone)

Morten Orregaard Nielsen

Queen's University - Department of Economics ( email )

94 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://www.econ.queensu.ca/faculty/nielsen/

Margit Sommer

School of Economics and Management, University of Aarhus ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

School of Economics and Management ( email )

Building 350
DK-8000 Aarhus C
Denmark

CREATES Research Papers ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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