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Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations

Author

Listed:
  • Olena Dehtiar
  • Yuliya Mishura
  • Kostiantyn Ralchenko

Abstract

We consider a stochastic differential equation of the form drt=(a−brt)dt+σrtdWt, where a, b and σ are positive constants. The solution corresponds to the Cox–Ingersoll–Ross process. We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path {rt,t∈[0,T]}. First, we prove the strong consistency of the maximum likelihood estimator. Since this estimator is well-defined only in the case 2a>σ2, we propose another estimator that is defined and strongly consistent for all positive a, b, σ. The quality of the estimators is illustrated by simulation results.

Suggested Citation

  • Olena Dehtiar & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(19), pages 6818-6833, October.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:19:p:6818-6833
    DOI: 10.1080/03610926.2020.1866611
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