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

Rattiya Meesa, Ratinan Boonklurb () and Phiraphat Sutthimat ()
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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

Mathematics, 2025, vol. 13, issue 12, 1-9

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.

Keywords: characteristic function; 3/2 model; noncentral Chi-square; squared Bessel process; transition density function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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