Limiting Loss Distribution of Default and Prepayment for Loan Portfolios and Its Application in RMBS

This paper studies the joint distribution of the default and prepayment losses for a large portfolio of loans, based on a bottom-up approach. The repayment behaviors of loans in the portfolio are determined by both systematic and idiosyncratic risk factors and are conditionally independent given the systematic factors. The joint two-dimensional limit distributions of the portfolio default and prepayment losses are obtained, including the strong law of large numbers and the central limit theorem. A numerical study for the portfolio losses is performed for some simplified models. Finally, we conduct the empirical analysis on the residential mortgage-backed security (RMBS) based on Freddie Mac’s dataset. The empirical results reveal the impacts of different factors on the default and prepayment behaviors, and the distributions of the portfolio losses are simulated based on empirical estimation results to show its difference with the log-normal distributions.