Abstract
This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.
Similar content being viewed by others
References
Berger, A., M. Ciment, and J. Rogers. “Numerical Solution of a Diffusion Consumption Problem with a Free Boundary,”SIAM Journal of Numerical Analysis 12 (1975), 646–672.
Brennan, M.J., and E.S. Schwartz. “Savings Bonds, Retractable Bonds and Callable Bonds,”Journal of Financial Economics 5 (1977), 66–68.
Brennan, M. J., and E.S. Schwartz. “Determinants of GNMA Mortgage Prices,”AREUEA Journal 13 (1985), 209–228.
Buser, S.A., and P.H. Hendershott. “Pricing Default-Free Mortgages,”Housing Finance Review 3 (1984), 405–429.
Cox, J.C., J.E. Ingersoll, Jr., and S.A. Ross. “Duration and the Measurement of Basis Risk,”Journal of Business 52 (1979), 51–61.
Cox, J.C., J.E. Ingersoll, Jr., and S.A. Ross. “A Re-examination of Traditional Hypothesis about the Term Structure of Interest Rates,”Journal of Finance 36 (1981), 769–799.
Cox, J.C., J.E. Ingersoll, Jr., and S.A. Ross. “An Intertemporal General Equilibrium Model of Asset Prices,”Econometrica 53 (1985a), 363–384.
Cox, J.C., J.E. Ingersoll, Jr., and S.A. Ross. “A Theory of the Term-Structure of Interest Rates,”Econometrica 53 (1985b), 385–407.
Cox, J.C., and S.A. Ross, “The Valuation of Options for Alternative Stochastic Processes,”Journal of Financial Economics 3 (1976), 145–166.
Cunningham, D.F., and P.H. Hendershott. “The Pricing of FHA Mortgage Default Insurance,”Housing Finance Review 3 (1984), 373–392.
Dunn, K.B., and J.J. McConnell. “Valuation of GNMA Mortgage-Backed Securities,”Journal of Finance 36 (1981), 599–616.
Epperson, J.F., J.B. Kau, D.C. Keenan, and W.J. Muller, III. “Pricing Default Risk in Mortgages,”AREUEA Journal 13 (1985), 261–272.
Forsythe, G., and W. Wasow.Finite Difference Methods for Partial Differential Equations. John Wiley & Sons, New York, 1960.
Geske, R. “The Valuation of Compound Options,”Journal of Financial Economics 7 (1979), 63–81.
Hall, A. “Valuing the Mortgage Borrower's Prepayment Option,”AREUEA Journal 3 (1985), 229–247.
Hendershott, P., and R. Van Order. “Pricing Mortgages: An Interpretation of the Model and Results,”Journal of Financial Services Research 1 (1987), 19–56.
Hilliard, J.E., J.B. Kau, D.C. Keenan, and W.J. Muller, III. “Pricing a Class of American and European Path Dependent Securities,” Forthcoming,Management Science.
Kau, J.B., D.C. Keenan, and T. Kirn. “Default Probabilities for Mortgages,”Journal of Urban Economics 35 (1994), 278–296.
Kau, J.B., D.C. Keenan, and W.J. Muller, III. “An Option-Based Pricing Model of Private Mortgage Insurance,”Journal of Risk and Insurance, 60 (1993), 288–299.
Kau, J.B., D.C. Keenan, W.J. Muller, II, J.F. Epperson. “Option Theory and Floating-Rate Securities with a Comparison of Adjustable and Fixed-Rate Mortgages,”Journal of Business, 66 (1994), 595–618.
Kau, J.B., D.C. Keenan, W.J. Muller, II, and J.F. Epperson. “A Generalized Valuation Model for Fixed-Rate Residential Mortgages,”Journal of Money, Credit, and Banking 24 (1992), 279–299.
Kau, J.B., D.C. Keenan, W.J. Muller, II, and J.F. Epperson. “Pricing Commercial Mortgages and Their Mortgage-Backed Securities,”Journal of Real Estate Finance and Economics 3 (1990a), 333–356.
Kau, J.B., D.C. Keenan, W.J. Muller, II, and J.F. Epperson. “The Valuation and Analysis of Adjustable Rate Mortgages,”Management Science 36 (1990b), 1417–1431.
Kau, J.B., D.C. Keenan, W.J. Muller, II, and J.F. Epperson. “The Valuation and Securitization of Commercial and Multifamily Mortgages,”Journal of Banking and Finance 11 (1987), 525–546.
Merton, R.C. “Theory of Rational Option Pricing,”Bell Journal of Economics and Management Science 4 (1973), 141–183.
Mulherin, J.H., and W.J. Muller, III. “Volatile Interest Rates and the Divergence of Incentives in Mortgage Contracts,”Journal of Law, Economics and Organization 3 (1987), 99–115.
Mulherin, J.H., and W.J. Muller, III. “Resolution of Incentive Conflicts in the Mortgage Industry,”Journal of Real Estate Finance and Economics 1 (1988), 35–36.
Richtmyer, R., and K. Mortan.Difference Methods for Initial Value Problems. New York: Wiley, 1967.
Smith, C.W., Jr. “Option Pricing: A Review,”Journal of Financial Economics 3 (1976), 3–51.
Smith, C.W., Jr. “On the Theory of Financial Contracting,”Journal of Monetary Economics 6 (1980), 333–357.
Smith, C.W., Jr. “Pricing Mortgage Origination,”AREUEA Journal 10 (1982), 313–330.
Stulz, R.M., and H. Johnson. “An Analysis of Secured Debt,”Journal of Financial Economics 14 (1985), 500–522.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kau, J.B., Keenan, D.C., Muller, W.J. et al. The valuation at origination of fixed-rate mortgages with default and prepayment. J Real Estate Finan Econ 11, 5–36 (1995). https://doi.org/10.1007/BF01097934
Issue Date:
DOI: https://doi.org/10.1007/BF01097934