Parameter Estimation for the Square-Root Diffusions: Ergodic and Nonergodic Cases

This article deals with the problem of parameter estimation in the Cox-Ingersoll-Ross (CIR) model (X t ) t≥0. This model is frequently used in finance for example as a model for computing the zero-coupon bound price or as a dynamic of the volatility in the Heston model. When the diffusion parameter is known, the maximum likelihood estimator (MLE) of the drift parameters involves the quantities : and . At first, we study the asymptotic behavior of these processes. This allows us to obtain various and original limit theorems on our estimators, with different rates and different types of limit distributions. Our results are obtained for both cases : ergodic and nonergodic diffusion. Numerical simulations were processed using an exact simulation algorithm. Keywords: Cox-Ingersoll-Ross processesLaplace transformLimit theoremsNonergodic diffusionParameter inferenceSimulation efficiencyMathematics Subject Classification: 44A1060F0562F1265C05 ACKNOWLEDGMENTS The authors are greatly indebted to the referees for their many suggestions of interesting references and for their helpful comments. This research was supported by the chair "Risques Financiers," Fondation du Risque.