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

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  • Stan Hurn

    ()
    (QUT)

  • Andrew McClelland

    ()
    (QUT)

  • Kenneth Lindsay

    ()
    (University of Glasgow)

Abstract

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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Bibliographic Info

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

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Keywords: stochastic differential equations; parameter estimation; quasi-maximum likelihood; moments;

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References

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  1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
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  7. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October.
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  9. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
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Cited by:
  1. Matyas Barczy & Gyula Pap & Tamas T. Szabo, 2014. "Parameter estimation for subcritical Heston models based on discrete time observations," Papers 1403.0527, arXiv.org.

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