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Stochastic Volatility

Author

Listed:
  • Torben G. Andersen

    () (Kellogg School of Management, Northwestern University, Evanston, IL; NBER, Cambridge, MA; and CREATES, Aarhus, Denmark)

  • Luca Benzoni

    (Federal Reserve Bank of Chicago, Chicago, Illinois, USA.)

Abstract

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.

Suggested Citation

  • Torben G. Andersen & Luca Benzoni, 2010. "Stochastic Volatility," CREATES Research Papers 2010-10, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-10
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    Keywords

    Stochastic Volatility; Realized Volatility; Implied Volatility; Options; Volatility Smirk; Volatility Smile; Dynamic Term Structure Models; Affine Models;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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