Uniform approximation of the Cox-Ingersoll-Ross process (Q2786430)

A simulation algorithm is developed for uniformly approximating the trajectories of the Cox-Ingersoll-Ross process \(V(t)\) defined as the solution of the stochastic differential equation NEWLINE\[NEWLINEdV(t)=k(\lambda-V(t))dt+\sigma\sqrt{V(t)}dw,\quad V(t_0)=V_0,NEWLINE\]NEWLINE where \(w\) is a scalar Brownian motion and \(k, \lambda,\sigma\) are positive constants. It is proved that the algorithm converges on any trajectory of \(V(t)\) that is positive on \([t_0,t_0+T]\). A modification of the algorithm is devised to deal with trajectories that get close to zero, and its convergence is proved. Numerical implementation is briefly discussed with emphasis on examples from Finance.