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We use Simulation based methods to construct improved estimation procedures for discretely observed diffusions. The benchmark model used for Illustration and comparison is the CKLS model for the short-term interest rate dr = κ(θ — r)dt -f arifW, where W is a Wiener process. Here, κ is the rate of mean-reversion, θ is the long term interest rate level, σ is a scaling parameter, and 7 is the constant elasticity of variance parameter. The likelihood function is unknown, and Standard methods of moments lead to biased and inconsistent estimates of the unknown parameters. Consistent estimates are obtained through a Simulation based correction of the estimating equations (Indirect Inference). The estimation methods are compared in a Monte Carlo study and in applications to different sets of U.S. data. We find that the Simulation based correction reduces the bias in parameter estimates, increases efficiency, and reduces bias in estimated Standard errors.

Monte Carlo Improvement of Estimates of the Mean-Reverting Constant Elasticity of Variance Interest Rate Diffusion