CALIBRATION OF THE UNI-VARIATE COX–INGERSOLL–ROSS MODEL AND PARAMETERS SELECTION THROUGH THE KULLBACK–LEIBLER DIVERGENCE

Abstract

This paper proposes a new estimation algorithm for the uni-variate Cox–Ingersoll–Ross (CIR) model in the state-space framework. The selection criterion among parameters is the likelihood but some parameters may have the same value; thus the initialization of the optimization routine is important especially if deterministic solvers are used. The algorithm aims at combining likelihood and two additional criteria based on the Kullback–Leibler divergence in order to find initial values in a grid search. The likelihood is then optimized in a restricted parameter set. A numerical experiment consists of generating data given a parameter set varying the length of the time series and the observation noise and then estimating the parameters with the algorithm. The results are discussed showing different performance levels for each parameter.