WIAS Preprint No. 2113, (2015)

Uniform approximation of the CIR process via exact simulation at random times


  • Milstein, Grigori N.
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 65C30 60H35


  • Cox-Ingersoll-Ross process, Sturm-Liouville problem, Bessel functions, confluent hypergeometric equation


In this paper we uniformly approximate the trajectories of the Cox-Ingersoll-Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact simulation of the CIR dynamics at some deterministic time grid.

Appeared in

  • Adv. Appl. Probab., 48 (2016) pp. 1095--1116.

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