Stochastic Volatility

55 Pages Posted: 21 Dec 2007 Last revised: 16 Jul 2010

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

Multiple version iconThere are 2 versions of this paper

Date Written: June 15, 2008


We give an overview of a broad class of models designed to capture stochastic volatility in financial markets, with illustrations of the scope of application of these models to practical finance problems. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process and is therefore a latent factor. These stochastic volatility specifications fit naturally in the continuous-time finance paradigm, and therefore serve as a prominent tool for a wide range of pricing and hedging applications. Moreover, the continuous-time paradigm of financial economics is naturally linked with the theory of volatility modeling and forecasting, and in particular with the practice of constructing ex-post volatility measures from high-frequency intraday data (realized volatility). One drawback is that in this setting volatility is not measurable with respect to observable information, and this feature complicates estimation and inference. Further, the presence of an additional state variable---volatility---renders the model less tractable from an analytic perspective. New estimation methods, combined with model restrictions that allow for closed-form solutions, make it possible to address these challenges while keeping the model consistent with the main properties of the data.

Keywords: Stochastic Volatility, Realized Volatility, Impled Volatility, Options, Smirk, Smile, Term Structure of Interest Rates, Affine Models

JEL Classification: E43, G12

Suggested Citation

Andersen, Torben G. and Benzoni, Luca, Stochastic Volatility (June 15, 2008). 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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