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.