On weak approximations of CIR equation with high volatility

We propose two new positive weak second-order approximations for the CIR equation dXt=(a−bXt)dt+σXtdBt based on splitting, at each step, the equation into the deterministic part dXt=(a−bXt)dt, which is solved exactly, and the stochastic part dXt=σXtdBt, which is approximated in distribution. The schemes are illustrated by encouraging simulation results.