On a two-phase minmax method for parameter estimation of the Cox, Ingersoll, and Ross interest rate model

In this paper we investigate a two-phase minmax optimization method for parameter estimation of the well known Cox, Ingersoll, and Ross one-factor interest rate model (CIR). In the first optimization phase we determine four CIR parameters by minimizing the sum of squares of differences of a theoretical CIR yield curve and real market yield curve data. We show that the minimum is attained on one dimensional curve in the four dimensional CIR parameter space. In order to find a global minimum we make use of a variant of an evolution strategy based minimization algorithm. Next we find a global maximum of the likelihood function restricted to this curve. We also introduce restricted maximum likelihood and nonlinear R² ratios measuring quality of estimation of the CIR parameters.