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; Phiraphat Sutthimat (Mathematics)
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.