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Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices

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Author Info

  • Peter Christoffersen
  • Kris Jacobs
  • Karim Mimouni

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on S&P500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared errors in- and out-of-sample.

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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 2007-37.

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Length: 37
Date of creation: 15 Nov 2007
Date of revision:
Handle: RePEc:aah:create:2007-37

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

Related research

Keywords: Stochastic volatility; option valuation; particle filtering; skewness; kurtosis; mean reversion;

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References

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Citations

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Cited by:
  1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
  2. Anders Tolver Jensen & Theis Lange, 2009. "On IGARCH and convergence of the QMLE for misspecified GARCH models," CREATES Research Papers 2009-06, School of Economics and Management, University of Aarhus.
  3. Malik, Sheheryar & Pitt, Michael K, 2009. "Modelling Stochastic Volatility with Leverage and Jumps : A Simulated Maximum Likelihood Approach via Particle Filtering," The Warwick Economics Research Paper Series (TWERPS) 897, University of Warwick, Department of Economics.

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