  In this paper, we consider the Cox--Ingersoll--Ross (CIR) process in the
regime where the process does not hit zero. We construct additive and
multiplicative discrete approximation schemes for the price of asset that is
modeled by the CIR process and geometric CIR process. In order to construct
these schemes, we take the Euler approximations of the CIR process itself but
replace the increments of the Wiener process with iid bounded vanishing
symmetric random variables. We introduce a "truncated" CIR process and apply it
to prove the weak convergence of asset prices. We establish the fact that this
"truncated" process does not hit zero under the same condition considered for
the original nontruncated process.
