Inference for Interest Rate Models Using Milstein’s Approximation
- 1 Department of Statistics, University of Manitoba, Winnipeg, Canada
- 2 Department of Statistics, University of Manitoba, Winnipeg, Canada
Abstract
A class of martingale estimating functions based on the first two moments of the observed process provides a conven ient 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 mar tingales 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 con tinuous-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 Cox Ingersoll-Ross interest rate model.
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