WIAS Preprint No. 1763, (2013)

Path-wise approximation of the Cox--Ingersoll--Ross process


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

2010 Mathematics Subject Classification

  • 65C30 60H35


  • Cox-Ingersoll-Ross process, Heston model, Doss-Sussmann formalism, exact simulation


The Doss-Sussmann (DS) approach is used for simulating the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows for expressing trajectories of the CIR process by solutions of some ordinary differential equation (ODE) that depend on realizations of the Wiener process involved. Via simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving an ODE, we approximately construct the trajectories of the CIR process. From a conceptual point of view the proposed method may be considered as an exact simulation approach.

Appeared in

  • Adv. Appl. Probab., 1132--1156 (2015) pp. .

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