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Mortgage Pricing: What Have We Learned So Far?

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  • Patric H. Hendershott

Abstract

Much progress has been achieved in the valuation of call options and interest-rate caps on default-free mortgages. The evidence suggests that the observed term structure of interest rates (the full structure, not just the end points) and a reasonable estimate of the volatility of spot rates is sufficient for pricing purposes. Knowledge of the precise nature of the interest-rate process and the exact market price of interest-rate risk, the not-well-identified determinants of the term structure, are not necessary for pricing. (The analogy to pricing stock options is striking; there, knowledge of the observed stock price -- and the present value of expected future dividends -- and a reasonable estimate of the volatility of the stock price are sufficient to price the option.) Moreover, the number of interest-rate state variables is also of little import, again holding the term structure and rate volatility constant. Pricing the mortgage default option, in contrast, is still in the embryonic stage. The stochastic process analogous to the interest-rate process in valuing call is a house price process: if a house price declines sufficiently, default occurs. The observed house price, the present value of expected future "dividends" (rents), and the volatility of house prices is, in principle, sufficient to value default (again note the analogy to stock price options). Unfortunately, rents are unknown, and no observable term-structure of expected future house-price inflation-rates exists from which to glean the division of expected housing returns between "dividends" and expected capital gains. Also, a series on the recent volatility of individual house prices is not readily available. Finally, measurement of the costs to defaulters and the losses of lenders/insurers when default occurs is far less straight-forward than is the case when call occurs or interest-rate caps are reached. (Here, an analogy can be drawn to the difficulties encountered in pricing the bankrupcy risk of firms.)

Suggested Citation

  • Patric H. Hendershott, 1986. "Mortgage Pricing: What Have We Learned So Far?," NBER Working Papers 1959, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:1959
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    1. Dunn, Kenneth B & McConnell, John J, 1981. "A Comparison of Alternative Models for Pricing GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(2), pages 471-484, May.
    2. Patric H. Hendershott & Sheng Cheng Hu & Kevin E. Villani, 1982. "The Economics of Mortgage Terminations: Implications for Mortgage Lenders and Mortgage Terms," NBER Working Papers 0918, National Bureau of Economic Research, Inc.
    3. Stephen A. Buser & Patric H. Hendershott, 1984. "The Pricing of Default-Free Mortgages," NBER Working Papers 1408, National Bureau of Economic Research, Inc.
    4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    5. Donald F. Cunningham & Patric H. Hendershott, 1984. "Pricing FHA Mortgage Default Insurance," NBER Working Papers 1382, National Bureau of Economic Research, Inc.
    6. Patric H. Hendershott & Sheng Hu, 1982. "Accelerating Inflation and Nonassumable Fixed-Rate Mortgages: Effects On Consumer Choice and Welfare," Public Finance Review, , vol. 10(2), pages 158-184, April.
    7. Brennan, Michael J. & Schwartz, Eduardo S., 1977. "Savings bonds, retractable bonds and callable bonds," Journal of Financial Economics, Elsevier, vol. 5(1), pages 67-88, August.
    8. James B. Kau & Donald C. Keenan & Walter J. Muller & James F. Epperson, 1985. "Rational Pricing of Adjustable Rate Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(2), pages 117-128, June.
    9. Patric H. Hendershott, 1985. "Pricing Adjustable Rate Mortgages," NBER Working Papers 1548, National Bureau of Economic Research, Inc.
    10. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    11. Arden R. Hall, 1985. "Valuing the Mortgage Borrower's Prepayment Option," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 229-247, September.
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    Cited by:

    1. Patric H. Hendershott & Thomas G. Thibodeau & Halbert C. Smith, 2009. "Evolution of the American Real Estate and Urban Economics Association1," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 37(4), pages 559-598, December.
    2. Stephen F. Thode & Richard J. Kish, 1994. "The Zero-Coupon/Interest-Only Fixed-Rate Mortgage: An Alternative for Funding Low-to-Moderate Income Housing," Journal of Real Estate Research, American Real Estate Society, vol. 9(2), pages 263-276.

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