Optimal Design of PAC-Companion Structure for Mortgage Backed Securities Using Cash Reserve

Owing to the agentification of the Government Housing Loan Corporation, Japanese private financial institutions are now developing long-term fixed-rate loans. In order to reduce the risk of yielding mismatches between asset and liability, financial institutions will sell out their loans by securitization instead of holding loans themselves. 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. In mortgage loans, borrowers are basically allowed to make prepayment. Repayment cash flow from a loan pool changes due to the prepayment. So there is a prepayment risk in MBS, which means that investors cannot invest excessive liquidity in a planned yield or duration when prepayment occurs faster than forecast. 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, which is unstable due to uncertainty of prepayment, 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, which will make it possible to issue more PAC bond. 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.