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

Author

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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)

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.

Suggested Citation

  • Llamazares-Elias Samir & Tocino Ángel Andrés, 2025. "Preservation of structural properties of the CIR model by θ-Milstein schemes," Monte Carlo Methods and Applications, De Gruyter, vol. 31(2), pages 163-171.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:2:p:163-171:n:1006
    DOI: 10.1515/mcma-2025-2009
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