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

Abstract

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.