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Maximum Likelihood Estimation of Stochastic Volatility Models

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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.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmg_pdfs/dp248.pdf
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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp248.

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Date of creation: Oct 1996
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Handle: RePEc:fmg:fmgdps:dp248

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Web page: http://www.lse.ac.uk/fmg/

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Cited by:
  1. George J. Jiang & Pieter J. van der Sluis, 1998. "Pricing Stock Options under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation," Tinbergen Institute Discussion Papers 98-067/4, Tinbergen Institute.
  2. Jun Yu & Zhenlin Yang & Xibin Zhang, 2002. "A Class of Nonlinear Stochastic Volatility Models and Its Implications on Pricing Currency Options," Monash Econometrics and Business Statistics Working Papers 17/02, Monash University, Department of Econometrics and Business Statistics.
  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. 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.
  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.
  6. Serigne N. Lo & Elvezio Ronchetti, 2006. "Robust Small Sample Accurate Inference in Moment Condition Models," Research Papers by the Department of Economics, University of Geneva 2006.04, Département des Sciences Économiques, Université de Genève.

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