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Stochastic Volatility

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  • 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 there- fore 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 mod- eling 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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-10.

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Length: 55
Date of creation: 25 Feb 2010
Date of revision:
Handle: RePEc:aah:create:2010-10

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Web page: http://www.econ.au.dk/afn/

Related research

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

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Cited by:
  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc.
  2. Peter F. Christoffersen & Francis X. Diebold, 1998. "How Relevant is Volatility Forecasting for Financial Risk Management?," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-080, New York University, Leonard N. Stern School of Business-.
  3. Patrick Asea & Mthuli Nube, 1997. "Heterogeneous Information Arrival and Option Pricing," UCLA Economics Working Papers 763, UCLA Department of Economics.
  4. Asea, Patrick K. & Ncube, Mthuli, 1998. "Heterogeneous information arrival and option pricing," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 291-323.
  5. Jacob Boudoukh & Matthew Richardson, 1999. "A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility," NBER Working Papers 7213, National Bureau of Economic Research, Inc.
  6. Mc Manus, Des & Watt, David, 1999. "Estimating One-Factor Models of Short-Term Interest Rates," Working Papers 99-18, Bank of Canada.
  7. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
  8. Francois-Éric Racicot & Raymond Théoret, 2011. "Forecasting stochastic Volatility using the Kalman filter: An Application to Canadian Interest Rates and Price-Earnings Ratio," RePAd Working Paper Series UQO-DSA-wp032011, Département des sciences administratives, UQO.
  9. Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc.

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