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Maximum likelihood estimation of stochastic volatility models

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  • Sandmann, G.
  • Koopman, Siem

Abstract

This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. 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 favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.

Suggested Citation

  • Sandmann, G. & Koopman, Siem, 1996. "Maximum likelihood estimation of stochastic volatility models," LSE Research Online Documents on Economics 119161, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:119161
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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. 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.
    3. 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".
    4. 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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    More about this item

    Keywords

    GARCH model; importance sampling; Kalman filter smoother; Monte Carlo simulation; quasi-maximum; stochastic volatility; unobserved components;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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