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O. Elerian, “A Note on the Existence of a Closed form Conditional Transition Density for the Milstein Scheme,” Economics Discussion Paper 1998-W18, Nuffield College, Oxford, 1998.

has been cited by the following article:

• TITLE: Inference for Interest Rate Models Using Milstein’s Approximation

  AUTHORS: Theodoro Koulis, Aera Thavaneswaran

  KEYWORDS: Interest Rate Models; Combined Estimating Functions; Information; Diffusion Processes; Milstein Approximation

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.1, February 28, 2013

  ABSTRACT: A class of martingale estimating functions based on the first two moments of the observed process provides a convenient framework for estimating the parameters of diffusion processes [1]. In the Bayesian set up, combined estimating functions had been studied for diffusion processes in [2] with filtering applications. However, when the conditional mean and the conditional variance are functions of parameters of interest in a diffusion process model, the basic martingales generating components of quadratic estimating functions are such that one is an absolute continuous function with respect to the other [3, p. 94]. Hence, the combined martingale estimating functions cannot be constructed for continuous-time diffusion processes. In this paper, a general framework for parameter estimation of discretely observed interest rate models is developed by using the Milstein approximation and closed form expressions for the information gain are also obtained. The method is used to study the estimates of the parameters for an extended version of the CoxIngersoll-Ross interest rate model.