Optimal design of PAC–companion structure for mortgage backed securities using cash reserve

Mortgage backed security (MBS) is a product of mortgage securitization, which is issued backed by the repayment cash flow from a loan pool consisting of many mortgage loans. Collateralized mortgage obligation (CMO) is a form of MBS, in which repayment cash flow from a loan pool is reorganized and bonds with various risks are issued. In this paper, we propose a method of designing CMO with PAC–companion structure. We divide repayment cash flow into two parts; a part in which principal repayment schedule must be satisfied (planned amortization class, PAC) and an unstable high-prepayment risk part (companion). We allow the repaid cash to be reserved in order to repay PAC bondholders in the following periods. We formulate the problem of determining an optimal PAC–companion structure as a mathematical programming problem and use a simulation-based approach to approximate the problem. We show that our model can be reformulated as an equivalent linear programming problem. Furthermore, we propose a modified model which yields a higher performance than the basic model. Finally we conduct numerical experiments and report the results.