On weak approximations of CIR equation with high volatility

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

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