Abstract
A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.
The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.
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References
Archer, Wayne R., and David C. Ling. (1993). “Pricing Mortgage-Backed Securities: Integrating Optimal Call Empirical Models of Prepayment,” Journal of the american Real Estate and Urban Economics Association 21(4), 373–404.
Brennan, Michael J., and Eduardo S. Schwartz. (1985). “Determinants of GNMA Mortgage Prices,” Journal of the American Real Estate and Urban Economics Association 13(3), 209–228.
Buser, Stephen A., and Patric H. Hendershott. (1984). “Pricing of Default-Free Mortgages,” Housing Finance Review 3 (October), 405–429.
Chang, Carolyn W., and Jack S.K. Chang. (1991). “Binomial Pricing: A Generalization,” Working paper, University of Southern California.
Chen, Andrew H., and David C. Ling. (1989). “Optimal Mortgage Refinancing with Stochastic Interest Rates,” Journal of the American Real Estate and Urban Economics Association 17(3), 278–299.
Chen, Ren-Raw, and T.L. Tyler Yang. (1995). “The Relevance of Interest Rate Processes in Pricing Mortgage-Backed Securities,” Journal of Housing Research 6(2), 315–332.
Cox, John C., Jonathan E. Ingersoll, and Steve A. Ross. (1985). “A Theory of the Term Structure of Interest Rates,” Econometrica 53(2), 385–407.
Cox, John C., Jonathan E. Ingersoll, and Steve A. Ross. (1981). “A Reexamination of Traditional Hypothesis About the Term Structure of Interest Rates,” Journal of Finance 36(4), 769–799.
Dunn, Kenneth B., and John J. McConnell. (1981). “Valuation of GNMA Mortgage Backed Securities,” Journal of Finance 36(3), 599–616.
Dunn, Kenneth B., and Chester S. Spatt. (1988a). “Call Options, Points and Dominance Restrictions on Debt Contracts,” Working paper, Carnegie Mellon University.
Dunn, Kenneth B., and Chester S. Spatt. (1988b). “Private Information and Incentives: Implications for Mortgage Contract Terms and Pricing,” Journal of Real Estate Finance and Economics 1(1), 47–60.
Follain, James R., and Dan-Nein Tzang. (1988). “The Interest Rate Differential and Refinancing a Home Mortgage,” The Appraisal Journal 61, 243–251.
Follain, James R., Louis O. Scott, and T.L. Tyler Yang. (1992). “Microfoundations of a Mortgage Prepayment Function,” Journal of Real Estate Finance and Economics 5(2), 197–217.
Green, Jerry, and John B. Shoven. (1986). “The Effects of Interest Rates on Mortgage Prepayments,” Journal of Money, Credit, and Banking 18(1), 41–59.
Hall, Arden R. (1985). “Valuing the Mortgage Borrower's Prepayment Option,” Journal of the American Real Estate and Urban Economics Association 13(3), 229–247.
Kau, James B., Donald C. Keenan, Walter Muller III, and James F. Epperson. (1992). “A Generalized Valuation Model for Fixed-Rate Residential Mortgages,” Journal of Money, Credit and Banking 24(3), 279–299.
Kau, James B., Donald C. Keenan, Walter Muller III, and James F. Epperson. (1995). “The Valuation at Origination of Fixed Rate Mortgages with Default and Prepayment,” Journal of Real Estate Finance and Economics 11(1), 5–36.
Kau, James B., Donald C. Keenan, and Taewon Kim. (1993). “Transaction Costs, Suboptimal Termination and Default Probabilities,” Journal of the American Real Estate and Urban Economics Association 21(3), 247–263.
Schwartz, Eduardo, and Walter Torous. (1992). “Prepayment, Defeult and the Valuation of Mortgage Pass-Through Securities,” Journal of Business 65(2), 221–239.
Stanton, Richard. (1995). “Rational Prepayment and the Valuation of Mortgage-Backed Securities,” Review of Financial Studies, Forthcoming.
Titman, Sheridan, and Walter Torous. (1989). “Valuing Commercial Mortgages: An Empirical Investigation of the Contingent-Claims Approach to Pricing Risky Debt,” Journal of Finance 44(2), 345–373.
Yang, T.L. Tyler. (1992). “Self-Selection in the Fixed Rate Mortgage Market,” Journal of the American Real Estate and Urban Economics Association 20(3), 359–391.
Yang, T.L. Tyler, and Brian A. Maris. (1993). “Mortgage Refinancing with Asymmetric Information,” Journal of the American Real Estate and Urban Economics Association 21(4), 481–510.
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Yang, T.T., Maris, B.A. Mortgage prepayment with an uncertain holding period. J Real Estate Finan Econ 12, 179–194 (1996). https://doi.org/10.1007/BF00132266
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DOI: https://doi.org/10.1007/BF00132266