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A note on the existence of a closed form conditional transition density for the Milstein scheme


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  • Ola Elerian
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    This paper is concerned with the estimation of stochastic differential equations when only discrete observations are available. It primarily focuses on deriving a closed form solution for the one-step ahead conditional transition density using the Milstein scheme. This higher order Taylor approximation enables us to obtain an order of improvement in accuracy in estimating the parameters in a non-linear diffusion, as compared to use of the Euler-Maruyama discretization scheme. Examples using simulated data are presented. The method can easily be extended to the situation where auxiliary points are introduced between the observed values. The Milstein scheme can be used to obtain the approximate transition density as in a Pedersen (1995) type of simulated likelihood method or within an MCMC method as propose din Elerian, Chib and Shephard (1998).

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    Bibliographic Info

    Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 1998-W18.

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    Date of creation: 01 Oct 1998
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    Handle: RePEc:oxf:wpaper:1998-w18

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    Keywords: Bayes estimation; nonlinear diffusion; Euler-Maruyama approximation; Maximum Likelihood; Markov chain Monte Carlo; Metropolis Hastings algorithm; Milstein scheme; Simulation; Stochastic Differential Equation.;


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    Cited by:
    1. Hurn, A.S. & Lindsay, K.A. & McClelland, A.J., 2013. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," Journal of Econometrics, Elsevier, vol. 172(1), pages 106-126.
    2. Michael W. Brandt & Pedro Santa-Clara, 2001. "Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets," NBER Technical Working Papers 0274, National Bureau of Economic Research, Inc.


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