A Direct Inversion Method for Chi-Square Sampling, Squared Bessel Processes, and Related Applications

This study proposes a new direct inversion method for simulating squared Bessel processes, which can efficiently and accurately generate non-central chi-square variables for any degrees of freedom, including small degrees of freedom scenarios that are computationally challenging. The method can generate non-central chi-square samples across the full range of degrees of freedom using the same set of Chebyshev coefficients, making it suitable for model calibration and supporting efficient and accurate simulation of CIR processes.