Preservation of structural properties of the CIR model by {\theta}-Milstein schemes
The ability of $\theta$-Milstein methods with $\theta\ge 1$ to capture the non-negativity and the mean-reversion property of the exact solution of the CIR model is shown. In addition, the order of convergence and the preservation of the long-term variance is studied. These theoretical results are illustrated with numerical examples.
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