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Pricing Default Risk in Mortgages

Author

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  • James F. Epperson
  • James B. Kau
  • Donald C. Keenan
  • Walter J. Muller

Abstract

This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment.Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions.The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined.The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper. Copyright American Real Estate and Urban Economics Association.

Suggested Citation

  • James F. Epperson & James B. Kau & Donald C. Keenan & Walter J. Muller, 1985. "Pricing Default Risk in Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 261-272.
  • Handle: RePEc:bla:reesec:v:13:y:1985:i:3:p:261-272
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    Citations

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    Cited by:

    1. Tyler Yang & Che-Chun Lin & Man Cho, 2011. "Collateral Risk in Residential Mortgage Defaults," The Journal of Real Estate Finance and Economics, Springer, vol. 42(2), pages 115-142, February.
    2. Lin, Che-Chun & Prather, Larry J. & Chu, Ting-Heng & Tsay, Jing-Tang, 2013. "Differential default risk among traditional and non-traditional mortgage products and capital adequacy standards," International Review of Financial Analysis, Elsevier, vol. 27(C), pages 115-122.
    3. Nicholas Sharp & David Newton & Peter Duck, 2008. "An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options," The Journal of Real Estate Finance and Economics, Springer, vol. 36(3), pages 307-342, April.
    4. Xudong An & John Clapp & Yongheng Deng, 2010. "Omitted Mobility Characteristics and Property Market Dynamics: Application to Mortgage Termination," The Journal of Real Estate Finance and Economics, Springer, vol. 41(3), pages 245-271, October.
    5. Seung Dong You, 2014. "The Leveraged City," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(4), pages 1042-1066, December.
    6. Ming Pu & Gang-Zhi Fan & Yongheng Deng, 2014. "Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry," The Journal of Real Estate Finance and Economics, Springer, vol. 48(3), pages 492-521, April.
    7. Leon G. Shilton & James R. Webb, 1989. "Commercial Loan Underwriting and Option Valuation," Journal of Real Estate Research, American Real Estate Society, vol. 4(1), pages 1-12.
    8. Reamonn Lyndon & Yvonne McCarthy, 2013. "What Lies Beneath? Understanding Recent Trends in Irish Mortgage Arrears," The Economic and Social Review, Economic and Social Studies, vol. 44(1), pages 117-150.
    9. Gordon W. Crawford & Eric Rosenblatt, 1995. "Efficient Mortgage Default Option Exercise: Evidence from Loss Severity," Journal of Real Estate Research, American Real Estate Society, vol. 10(5), pages 543-556.
    10. Patric H. Hendershott & Thomas G. Thibodeau & Halbert C. Smith, 2009. "Evolution of the American Real Estate and Urban Economics Association-super-1," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 37(4), pages 559-598.
    11. Terrence Clauretie & Nasser Daneshvary, 2011. "The Optimal Choice for Lenders Facing Defaults: Short Sale, Foreclose, or REO," The Journal of Real Estate Finance and Economics, Springer, vol. 42(4), pages 504-521, May.
    12. Dejun Xie, 2009. "A Steady State Solution to a Mortgage Pricing Problem," Papers 0909.5389, arXiv.org.
    13. Andrey Pavlov & George Blazenko, 2005. "The Neighborhood Effect of Real Estate Maintenance," The Journal of Real Estate Finance and Economics, Springer, vol. 30(4), pages 327-340, June.
    14. Patric H. Hendershott & Robert Van Order, 1987. "Pricing Mortgages: An Interpretation of the Models and Results," NBER Working Papers 2290, National Bureau of Economic Research, Inc.
    15. Foote, Christopher L. & Willen, Paul S., 2017. "Mortgage-default research and the recent foreclosure crisis," Working Papers 17-13, Federal Reserve Bank of Boston.
    16. Barry Dennis & Chionglong Kuo & Tyler Yang, 1997. "Rationales of Mortgage Insurance Premium Structures," Journal of Real Estate Research, American Real Estate Society, vol. 14(3), pages 359-378.
    17. Richard J. Buttimer, 2011. "The financial crisis: imperfect markets and imperfect regulation," Journal of Financial Economic Policy, Emerald Group Publishing, vol. 3(1), pages 12-32, April.
    18. Dennis Capozza & Thomas Thomson, 2006. "Subprime Transitions: Lingering or Malingering in Default?," The Journal of Real Estate Finance and Economics, Springer, vol. 33(3), pages 241-258, November.
    19. Gregory Connor & Thomas Flavin, 2013. "Irish Mortgage Default Optionality," Economics, Finance and Accounting Department Working Paper Series n243-13.pdf, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.
    20. Paul Carrillo, 2013. "Testing for Fraud in the Residential Mortgage Market: How Much Did Early-Payment-Defaults Overpay for Housing?," The Journal of Real Estate Finance and Economics, Springer, vol. 47(1), pages 36-64, July.
    21. Terrence M. Clauretie & Mel Jameson, 1995. "Residential Loan Renegotiation: Theory and Evidence," Journal of Real Estate Research, American Real Estate Society, vol. 10(2), pages 153-162.
    22. Luci Ellis, 2010. "The Housing Meltdown: Why Did It Happen in the United States?," International Real Estate Review, Asian Real Estate Society, vol. 13(3), pages 351-394.
    23. Eddie Lam, 2002. "A Risk Management Model for MBS Issuers," International Real Estate Review, Asian Real Estate Society, vol. 5(1), pages 169-195.
    24. 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.
    25. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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