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A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

  • Stan Hurn

    ()

    (QUT)

  • Andrew McClelland

    ()

    (QUT)

  • Kenneth Lindsay

    ()

    (University of Glasgow)

This paper develops a quasi-maximum likelihood (QML) procedure for estimating the parameters of multi-dimensional stochastic differential equations. The transitional density is taken to be a time-varying multivariate Gaussian where the first two moments of the distribution are approximately the true moments of the unknown transitional density. For affine drift and diffusion functions, the moments are shown to be exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good. The estimation procedure is easily generalizable to models with latent factors, such as the stochastic volatility class of model. The QML method is as effective as alternative methods when proxy variables are used for unobserved states. A conditioning estimation procedure is also developed that allows parameter estimation in the absence of proxies.

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File URL: http://www.ncer.edu.au/papers/documents/WPNo65.pdf
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Paper provided by National Centre for Econometric Research in its series NCER Working Paper Series with number 65.

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Length: 35 pages
Date of creation: 28 Oct 2010
Date of revision:
Handle: RePEc:qut:auncer:2010_12
Contact details of provider: Phone: 07 3138 5066
Fax: 07 3138 1500
Web page: http://www.ncer.edu.au

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  6. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
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  11. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
  12. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
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