Credit portfolio modeling and pricing using the Poisson binomial distribution

Bilgi Yilmaz and Alper Hekimoglu

Abstract

This study extends the Poisson binomial distribution by introducing correlation and dependence between binomial events, enhancing its ability to capture complex event types and improving model validation, which could turn this theoretical statistical method into a tool for actuarial science and financial statistics. The study integrates Gaussian copula and shifted-gamma copula (factor decomposition) models into the Poisson binomial distribution framework, enabling the valuation of credit portfolios with tranches without relying on large homogeneous portfolio approximation. Monte Carlo simulations validate the derived formulas and demonstrate the improvement in accuracy achieved by considering varying default-probability parameters for each client. The practical application of the proposed approach is illustrated through credit portfolio tranche pricing, highlighting the sensitivity of credit portfolios to dependence. Moreover, the study explores an efficient and straightforward implementation of the Poisson binomial distribution by incorporating and refining an approach to discrete Fourier transform representation from a 2013 paper by Hong. Our proposal achieves reductions in computational cost compared with the method proposed by Hong.