Rate of convergence of discretized drift parameters estimators in the Cox–Ingersoll–Ross model

Abstract

The article is devoted to the drift parameters estimation in the Cox–Ingersoll–Ross model. We obtain the rate of convergence in probability of the maximum likelihood estimators based on the continuous-time estimators. Then we introduce the discrete versions of these estimators and investigate their asymptotic behavior. In particular, we establish the conditions for weak and strong consistency, asymptotic normality, and get the rate of convergence in probability.

Keywords:

• Asymptotic normality
• Cox–Ingersoll–Ross model
• continuous observations
• discrete observations
• parameter estimation
• rate of convergence
• strong consistency

Acknowledgments

The authors are grateful to the anonymous referee for valuable comments and suggestions. Kostiantyn Ralchenko is grateful to his hosts at Macquarie University, where he was a Visiting Fellow sponsored by Sydney Mathematical Research Institute (SMRI).

Additional information

Funding

The research by Yuliya Mishura has been supported by the Swedish Foundation for Strategic Research, grant no. UKR22–0017. The research by Yuliya Mishura and Kostiantyn Ralchenko was carried through within the frame and support of the ToppForsk project no. 274410 “STORM: Stochastics for Time-Space Risk Models” granted by the Research Council of Norway.