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Maximum Likelihood Estimation of Stochastic Volatility Models

Listed author(s):
  • G Sandmann
  • Siem Jan Koopman

This paper presents a Monte Carlo maximum likelihood method of estimating Stochastic Volatility (SV). The basic SV model can be expressed as a linear state space model with log chi-square disturbances. Assuming the Gaussianity of these disturbances, application of the Kalman filter leads to consistent but inefficient Quasi- Maximum Likelihood (QML) estimation. Addressing this problem the present paper shows how arbitrarily close approximations to the exact likelihood function can be constructed by means of importance sampling. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favourably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Markov Chain Monte Carlo (MCMC) method.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmg_pdfs/dp248.pdf
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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp248.

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Date of creation: Oct 1996
Handle: RePEc:fmg:fmgdps:dp248
Contact details of provider: Web page: http://www.lse.ac.uk/fmg/

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  1. Torben G. Andersen & Hyung-Jin Chung & Bent E. Sorensen, "undated". "EMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Computing in Economics and Finance 1997 6, Society for Computational Economics.
  2. Lamoureux, Christopher G & Lastrapes, William D, 1990. " Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
  3. repec:cep:stiecm:/1993/268 is not listed on IDEAS
  4. Andrew C Harvey & N.G. Shephard, 1993. "Estimation and Testing of Stochastic Variance Models," STICERD - Econometrics Paper Series 268, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  6. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
  7. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
  8. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers 95-36, Duke University, Department of Economics.
  9. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
  10. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  11. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  12. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
  13. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
  15. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
  16. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
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