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Maximum Likelihood Estimation of Stochastic Volatility Models

Author

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  • G Sandmann
  • Siem Jan Koopman

Abstract

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.

Suggested Citation

  • G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group.
  • Handle: RePEc:fmg:fmgdps:dp248
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    References listed on IDEAS

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    Cited by:

    1. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    2. Serigne N. Lo & Elvezio Ronchetti, 2006. "Robust Small Sample Accurate Inference in Moment Condition Models," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2006.04, Institut d'Economie et Econométrie, Université de Genève.
    3. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    4. Roberto Casarin & Domenico Sartore, 2007. "Matrix-State Particle Filter for Wishart Stochastic Volatility Processes," Working Papers 2007_30, Department of Economics, University of Venice "Ca' Foscari".
    5. Kleppe, Tore Selland & Skaug, Hans J., 2008. "Simulated maximum likelihood for general stochastic volatility models: a change of variable approach," MPRA Paper 12022, University Library of Munich, Germany.

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