Preservation of structural properties of the CIR model by θ-Milstein schemes

Llamazares-Elias Samir () and Tocino Ángel Andrés ()
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Llamazares-Elias Samir: Department of Mathematics, University of Salamanca, Pl. Merced, 1, 37008 Salamanca, Spain
Tocino Ángel Andrés: Department of Mathematics, University of Salamanca, Pl. Merced, 1, 37008 Salamanca, Spain

Monte Carlo Methods and Applications, 2025, vol. 31, issue 2, 163-171

Abstract: The ability of θ-Milstein methods with θ ≥ 1 {\theta\geq 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.

Keywords: CIR model; mean-reversion; non-negativity; stochastic numerical method; implicit Milstein (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2025-2009

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