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On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process

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  • Rattiya Meesa

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Ratinan Boonklurb

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Phiraphat Sutthimat

    (Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
    Financial Mathematics, Data Science and Computational Innovations Research Unit (FDC), Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand)

Abstract

We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally, we demonstrate that the same approach extends to a broad family of non-affine, time-varying diffusions, providing a general framework for obtaining transition PDFs and moments in advanced models.

Suggested Citation

  • Rattiya Meesa & Ratinan Boonklurb & Phiraphat Sutthimat, 2025. "On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process," Mathematics, MDPI, vol. 13(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1948-:d:1677120
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    References listed on IDEAS

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