Efficient Risk Analysis of Mortgage Pools

Abstract

Financial institutions, government-sponsored enterprises such as Fannie Mae, and asset-backed security investors are often exposed to delinquency and prepayment risk from large numbers of loans. Examples include mortgages, credit cards, auto, commercial, real estate, student, and small business loans. Due to the size of such loan pools and the potentially long maturities of their cashflows, the measurement and management of these exposures is computationally expensive. This paper develops and tests efficient numerical methods for the risk analysis of large pools of loans. For a broad class of dynamic loan-level models of delinquency and prepayment, we develop a law of large numbers and a central limit theorem for the loss and prepayment levels in the pool. The asymptotics are then used to construct efficient Monte Carlo approximations of the loss and prepayment distributions for a large pool. The approximations aggregate the full loan-level dynamics, making it possible to take advantage of the detailed loan-level data often available. The Monte Carlo approximation allows for efficient risk analysis of loan portfolios as well as MBSs, CMOs, and other ABSs backed by pools of loans. To demonstrate the effectiveness of our approach, we implement it on a data set of over 25 million actual subprime and agency mortgages. The results show the accuracy and speed of the approximation in comparison to brute-force simulation of a pool, for a variety of pools with different risk characteristics. Computational cost is often several orders of magnitude less than brute-force simulation of the actual pool with a similar level of accuracy. Furthermore, the computational expense of our efficient Monte Carlo approximation is constant no matter the dimension of the loan-level features; this is key since loan-level feature data is often high-dimensional.