Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2005-009 (August 19, 2005)

An Optimal Design of Collateralized Mortgage Obligation with PAC-Companion Structure Using Dynamic Cash Reserve
by Da-shan Huang, Yoshitaka Kai, Frank J. Fabozzi and Masao Fukushima

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This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool's cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC's scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved effciently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model.