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An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve. (English) Zbl 1109.90064

Summary: 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 efficiently. 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.

MSC:

90C15 Stochastic programming
90C05 Linear programming
91B30 Risk theory, insurance (MSC2010)

Software:

SeDuMi
Full Text: DOI

References:

[1] Cox, J. C.; Ingersoll, J. E.; Ross, S. A., A theory of the term structure of interest rates, Econometrica, 53, 2, 383-408 (1985)
[2] Fabozzi, F. J.; Ramsey, C., Collateralized Mortgage Obligations: Structures and Analysis (1999), John Wiley & Sons
[3] Kariya, T.; Kobayashi, M., Pricing mortgage-backed securities (MBS) - a model describing the burnout effect, Asia-Pacific Financial Markets, 7, 2, 189-204 (2000) · Zbl 1153.91425
[4] Kariya, T., Ushiyama, F., Pliska, S.R., 2002. A 3-factor valuation model for mortgage-back securities (MBS). Technical Paper, Kyoto Institute of Ecomonic Research. Available from: <http://www.kier.kyoto-u.ac.jp/ kariya/papers/TK_papers_en075.html; Kariya, T., Ushiyama, F., Pliska, S.R., 2002. A 3-factor valuation model for mortgage-back securities (MBS). Technical Paper, Kyoto Institute of Ecomonic Research. Available from: <http://www.kier.kyoto-u.ac.jp/ kariya/papers/TK_papers_en075.html
[5] Kau, J. B.; Keenan, D. C.; Muller, W. J.; Epperson, J. F., A generalized valuation model for fixed-rate residential mortgages, Journal of Money, Credit and Banking, 24, 3, 279-299 (1992)
[6] Kau, J. B.; Keenan, D. C.; Muller, W. J.; Epperson, J. F., The valuation at origination of fixed-rate residential mortgages with default and prepayment, Journal of Real Estate Finance and Economics, 11, 1, 5-39 (1995)
[7] Kutsuna, T., Kai, Y., Fukushima, M., 2004. Optimal design of PAC-companion structure for mortgage backed securities using cash reserve. Preprint (in Japanese).; Kutsuna, T., Kai, Y., Fukushima, M., 2004. Optimal design of PAC-companion structure for mortgage backed securities using cash reserve. Preprint (in Japanese).
[8] Luo, Z. Q.; Pang, J. S.; Ralph, D., Mathematical Programs with Equilibrium Constraints (1996), Cambridge University Press
[9] Schwartz, E. S.; Torous, W. N., Prepayment and the variation of mortgage-backed securities, Journal of Finance, 44, 2, 375-392 (1989)
[10] Stanton, R., Rational prepayment and the value of mortgage-backed securities, The Review of Financial Studies, 8, 3, 677-708 (1995)
[11] Sturm, J., 2001. Using seDuMi, a matlab toolbox for optimization over symmetric cones. Technical Paper, Department of Econometrics. Tilburg University, The Netherlands. Available from: <http://www.optimization-online.org/DB-HTML/2001/10/395.html; Sturm, J., 2001. Using seDuMi, a matlab toolbox for optimization over symmetric cones. Technical Paper, Department of Econometrics. Tilburg University, The Netherlands. Available from: <http://www.optimization-online.org/DB-HTML/2001/10/395.html
[12] Vanderbei, R. J., Linear Programming: Foundations and Extensions (1996), Kluwer Academic Publishers · Zbl 0874.90133
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