Realized Volatility

29 Pages Posted: 12 Feb 2008 Last revised: 5 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

Luca Benzoni

Federal Reserve Bank of Chicago - Research Department

Date Written: July 22, 2008


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.

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

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

Suggested Citation

Andersen, Torben G. and Benzoni, Luca, Realized Volatility (July 22, 2008). FRB of Chicago Working Paper No. 2008-14, Available at SSRN: or

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

Aarhus University - 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)


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