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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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