Credit portfolio modeling and pricing using the Poisson binomial distribution

This study extends the Poisson binomial distribution by introducing correlation anddependence between binomial events, enhancing its ability to capture complex eventtypes and improving model validation, which could turn this theoretical statisticalmethod into a tool for actuarial science and financial statistics. The study integratesGaussian copula and shifted-gamma copula (factor decomposition) models into thePoisson binomial distribution framework, enabling the valuation of credit portfolioswith tranches without relying on large homogeneous portfolio approximation. MonteCarlo simulations validate the derived formulas and demonstrate the improvementin accuracy achieved by considering varying default-probability parameters for eachclient. The practical application of the proposed approach is illustrated through creditportfolio tranche pricing, highlighting the sensitivity of credit portfolios to depend-ence. Moreover, the study explores an efficient and straightforward implementationof the Poisson binomial distribution by incorporating and refining an approach to discrete Fourier transform representation from a 2013 paper by Hong. Our proposalachieves reductions in computational cost compared with the method proposed byHong.