Abstract
We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.
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References
Bielecki, T. R. and Rutkowski, M. (2001) Credit Risk: Modeling, Valuation and Hedging, Springer Finance,
Collin-Dufresne, P., Goldstein, R. S. and Helwege, J. (2003) Is Credit Event Risk Priced? Modeling Contagion via the Updating of Beliefs. Working paper.
Deng, Y. and Quigley, J. (2001) Woodhead Behavior and the Pricing of Residential Mortgages. Berkeley Program on Housing and Urban Policy, Working paper Series W00-004.
Downing, C., Stanton, R. and Wallace, N. (2003) An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter? Working paper.
Duffie, D. and Lando, D. (2001) Term Structure of Credit Spreads with Incomplete Accounting Information, Econometrica 69, 633–664.
Dunn, K. B. and McConnell, J. J. (1981a) A Comparison of Alternative Models for Pricing GNMA Mortgage-Backed Securities, Journal of Finance 36, 471–483.
Dunn, K. B. and McConnell, J. J. (1981b) Valuation of Mortgage-Backed Securities, Journal of Finance 36, 599–617.
Dunn, K. B. and Spatt, C. S. (1986) The Effect of Refinancing Costs and Market Imperfections on Optimal Call Strategy and the Pricing of Debt Contracts. Working Paper: Carnegie-Mellon University.
Durrett, R. (1995) Probability, Theory and Examples, 2nd. ed. Duxbury Press.
Frey, R. and McNeil, A. J. (2003) Dependent Defaults in Models of Portfolio Credit Risk, Journal of Risk 6, 59–92.
Giesecke, K. and Goldberg, L. R. (2004) Forecasting Default in the Face of uncertainty. Journal of Derivatives 25
Giesecke, K. and Goldberg, L. R. (2003) The Market Price of Credit Risk. Working paper.
Goncharov, Y. (2002) An Intensity-Based Approach for Valuation of Mortgage Contracts Subject to Prepayment Risk, Working paper.
Ichijo, H. (2003) Prepayment rate model of mortgage that unites structural approach and reduced-form approach. Proceedings of the 19th JAFEE Conference, 188–207 (written in Japanese).
Ichijo, H. and Moridaira, S. (2001) Prepayment analyses of mortgage. Proceedings of the 15th JAFEE Conference, pp. 221–239 (written in Japanese).
Jarrow, R. A., Lando, D. and Yu, F. (2005) Default risk and diversification: Theory and empirical implications, Mathematical Finance 15, 1–26.
Jeanblanc, M. and Rutkowski, M. (2000)Modelling of Default Risk: Mathematical tools. Working Paper.
Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. Springer-Verlag, New York.
Kariya, T. and Kobayashi, M. (2000) Pricing mortgage-backed securities (MBS), Asia-Pacific Financial Markets 7, 189–204.
Kariya, T., Pliska, S. R. and Ushiyama, F. (2002) A 3-factor Valuation Model for Mortgage-Backed Securities (MBS). Working Paper.
Leblanc, B. and Renault, O. and Scaillet, O. (2000) A correction note on the first passage time of an Ornstein-Uhlenbech Process to a boundary, Finance and Stochastics 4, 109–111.
Lyuu, Y. D. (2002) Financial Engineering and Computation. Cambridge.
McConnell, J. J. and Singh, M. (1994) Rational prepayment and the valuation of Collateralized Mortgage Obligations, Journal of Finance 49 891–921.
Nakagawa, N. and Shouda, T. (2004) Valuation of Mortgage-Backed Securities Based on Unobservable Prepayment Costs, Advances in Mathematical Economics 6, 123–147.
Nakamura, N. (2001) Valuation of Mortgage-Backed Securities Based upon a Structural Approach, Asia-Pacific Financial Markets 8, 259–289.
Nakamura, N. and Shibasaki, K. (2001) Valuation of Mortgage-Backed Securities Based upon a Hazard Rate Approach, The 15th JAFEE Conference Proceedings (Japanese).
Popova, E., Popova, I. and George, E. (2003) Bayesian Modeling of Mortgage Prepayment Rates, Working Paper.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1992) Numerical Recipes in C : The Art of Scientific Computing, 2nd ed. Cambridge University Press.
Protter, E. P. (2004) Stochastic Integration and Differential Equations 2nd ed. Springer.
Richard, S. F. and Roll. R. (1989) Prepayments on fixed-rate mortgage-backed securities, Journal of Portfolio Management 15 73–82.
Schwartz, E. S. and Torous, W. N. (1989) Prepayment and the Valuation of Mortgage-Backed Securities, Journal of Finance 44, 375–392.
Stanton, R. (1995) Rational prepayment and the Valuation of Mortgage-Backed Securities, Review of Financial Studies 8, 677–708.
Sugimura, T. (2002) A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach, Asia-Pacific Financial Markets 305–335.
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This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.
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Nakagawa, H., Shouda, T. Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes. Asia-Pacific Finan Markets 11, 233–266 (2004). https://doi.org/10.1007/s10690-005-9002-5
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DOI: https://doi.org/10.1007/s10690-005-9002-5