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On the numerical integration of the mean-reverting CEV model by θ-Milstein schemes

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  • Llamazares-Elias, Samir
  • Tocino, Angel

Abstract

The numerical approximation of the mean-reverting CEV equation using a class of semi-implicit Milstein schemes is studied. We focus on the preservation of the main structural properties of the exact solution of the CEV model: positivity and mean reversion. In addition, the conservation of the long-term second moment is shown for the particular case of the Brennan–Schwartz model. The results are compared analytically and numerically with those obtained for other schemes specially designed to integrate this model.

Suggested Citation

  • Llamazares-Elias, Samir & Tocino, Angel, 2026. "On the numerical integration of the mean-reverting CEV model by θ-Milstein schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 713-726.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:713-726
    DOI: 10.1016/j.matcom.2026.04.036
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    References listed on IDEAS

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    1. Kahl Christian & Schurz Henri, 2006. "Balanced Milstein Methods for Ordinary SDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 143-170, April.
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    6. Ioannis S. Stamatiou, 2021. "The Semi-discrete Method for the Approximation of the Solution of Stochastic Differential Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 625-638, Springer.
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    8. Nikolaos Halidias & Ioannis Stamatiou, 2015. "Approximating explicitly the mean reverting CEV process," Papers 1502.03018, arXiv.org, revised May 2015.
    9. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
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