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
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.