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Realized Volatility

Torben G. Andersen

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

Luca Benzoni

Federal Reserve Bank of Chicago - Research Department

July 22, 2008

FRB of Chicago Working Paper No. 2008-14

Realized volatility is a nonparametric ex-post estimate of the return variation. The most obvious realized volatility measure is the sum of finely-sampled squared return realizations over a fixed time interval. In a frictionless market the estimate achieves consistency for the underlying quadratic return variation when returns are sampled at increasingly higher frequency. We begin with an account of how and why the procedure works in a simplified setting and then extend the discussion to a more general framework. Along the way we clarify how the realized volatility and quadratic return variation relate to the more commonly applied concept of conditional return variance. We then review a set of related and useful notions of return variation along with practical measurement issues (e.g., discretization error and microstructure noise) before briefly touching on the existing empirical applications.

Number of Pages in PDF File: 29

Keywords: Realized Volatility, Stochastic Volatility, Quadratic Variation, Bipower Variation, Variance Swap, Impled Volatility

JEL Classification: G12, G13, C22, C32, C53

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Date posted: February 12, 2008 ; Last revised: December 5, 2008

Suggested Citation

Andersen, Torben G. and Benzoni, Luca, Realized Volatility (July 22, 2008). FRB of Chicago Working Paper No. 2008-14. Available at SSRN: https://ssrn.com/abstract=1092203 or http://dx.doi.org/10.2139/ssrn.1092203

Contact Information

Torben G. Andersen
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
University of Aarhus - CREATES ( email )
School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Luca Benzoni (Contact Author)
Federal Reserve Bank of Chicago - Research Department ( email )
230 South LaSalle Street
Chicago, IL 60604
United States
312-322-8499 (Phone)
HOME PAGE: http://lbenzoni.frbchi.googlepages.com/
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