Functional limit theorems for additive and multiplicative schemes in the Cox--Ingersoll--Ross model

摘要

In this paper, we consider the Cox--Ingersoll--Ross (CIR) process in theregime where the process does not hit zero. We construct additive andmultiplicative discrete approximation schemes for the price of asset that ismodeled by the CIR process and geometric CIR process. In order to constructthese schemes, we take the Euler approximations of the CIR process itself butreplace the increments of the Wiener process with iid bounded vanishingsymmetric random variables. We introduce a "truncated" CIR process and apply itto prove the weak convergence of asset prices. We establish the fact that this"truncated" process does not hit zero under the same condition considered forthe original nontruncated process.