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Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method

Author

Listed:
  • Isil Erol

    (Department of Economics, Middle East Technical University, Ankara-Turkey;)

  • Kanak Patel

    (Department of Land Economy, University of Cambridge, England;)

Abstract

This paper evaluates the default risk of civil servants’ wage-indexed payment mortgage (WIPM) contract in Turkey, which is linked to the expected inflation. The aim of the study has two sides: one is to apply the contingent claims approach, which has been widely used to price standard fixed- and adjustable-rate contracts, to price an inflation-indexed mortgage. The second is to understand if WIPM contract is a suitable mortgage design for lenders under an inflationary economy. We extend the traditional risk-neutral valuation for pricing the WIPM contract with its embedded default option. Using backward pricing method, namely the explicit finite difference method, we evaluate this unique nflation-indexed mortgage contract from the lender’s point of view. The expected inflation and house price are the two tochastic variables underlying the WIPM contract. Our numerical results show that the lender benefits from originating WIPM only during the periods when the real interest rate is very low. Expected inflation risk premium notably increases the value of future payments on WIPM contract, resulting in high values of lender’s position in the mortgage agreement. The results also show that house price volatility has a greater effect on the borrower’s default option value compared to the expected inflation volatility

Suggested Citation

  • Isil Erol & Kanak Patel, 2007. "Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method," International Real Estate Review, Global Social Science Institute, vol. 10(1), pages 48-92.
    • Handle: RePEc:ire:issued:v:010:n:01:2007:p:48-92
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    References listed on IDEAS

    as
    1. William H. Scott & Arthur L. Houston & A. Quang Do, 1993. "Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(1), pages 1-25, March.
    2. Baesel, Jerome B. & Biger, Nahum, 1980. "The Allocation of Risk: Some Implications of Fixed versus Index-Linked Mortgages," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(2), pages 457-468, June.
    3. Peter J. Elmer, 1992. "PLAM Default Risk," Journal of Real Estate Research, American Real Estate Society, vol. 7(2), pages 157-168.
    4. Kearl, J R, 1979. "Inflation, Mortgages, and Housing," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 1115-1138, October.
    5. José A. Azevedo‐Pereira & David P. Newton & Dean A. Paxson, 2002. "UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 30(2), pages 185-211.
    6. James B. Kau & Donald C. Keenan & Walter J. Muller & James F. Epperson, 1990. "The Valuation and Analysis of Adjustable Rate Mortgages," Management Science, INFORMS, vol. 36(12), pages 1417-1431, December.
    7. Stanton, Richard & Wallace, Nancy, 1999. "Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages," The Journal of Real Estate Finance and Economics, Springer, vol. 19(1), pages 49-67, July.
    8. Taewon Kim, 1987. "A Contingent Claims Analysis of Price Level‐Adjusted Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 15(3), pages 117-131, September.
    9. Hakan Berument & Kamuran Malatyali, 1999. "Determinants of interest rates in Turkey," Discussion Papers 9902, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    10. Ramaswamy, Krishna & Sundaresan, Suresh M., 1986. "The valuation of floating-rate instruments : Theory and evidence," Journal of Financial Economics, Elsevier, vol. 17(2), pages 251-272, December.
    11. Kau, James B & Keenan, Donald C & Muller, Walter J, III & Epperson, James F, 1993. "Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages," The Journal of Business, University of Chicago Press, vol. 66(4), pages 595-618, October.
    12. Richard Stanton & Nancy Wallace, 1995. "ARM Wrestling: Valuing Adjustable Rate Mortgages Indexed to the Eleventh District Cost of Funds," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 23(3), pages 311-345, September.
    13. Hakan Berument & Asli Günay, 2003. "Exchange Rate Risk and Interest Rate: A Case Study for Turkey," Open Economies Review, Springer, vol. 14(1), pages 19-27, January.
    14. Stephen A. Buser & Patric H. Hendershott, 1984. "The Pricing of Default-Free Mortgages," NBER Working Papers 1408, National Bureau of Economic Research, Inc.
    15. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    16. Gerald Buetow, Jr. & Joseph Albert, 1998. "The Pricing of Embedded Options in Real Estate Lease Contracts," Journal of Real Estate Research, American Real Estate Society, vol. 15(3), pages 253-266.
    17. Lea, Michael J. & Bernstein, Steven A., 1996. "Housing Finance in an Inflationary Economy: The Experience of Mexico1," Journal of Housing Economics, Elsevier, vol. 5(1), pages 87-104, March.
    18. Statman, Meir, 1982. "Fixed Rate or Index-Linked Mortgages from the Borrower's Point of View: A Note," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(3), pages 451-457, September.
    19. Erol, Isil & Patel, Kanak, 2005. "Default risk of wage-indexed payment mortgage in Turkey," Journal of Housing Economics, Elsevier, vol. 14(3), pages 271-293, September.
    20. Joseph B. Lipscomb & John T. Harvey & Harold Hunt, 2003. "Exchange-Rate Risk Mitigation with Price-Level-Adjusting Mortgages: The Case of the Mexican UDI," Journal of Real Estate Research, American Real Estate Society, vol. 25(1), pages 23-42.
    21. repec:bla:jfinan:v:44:y:1989:i:2:p:345-73 is not listed on IDEAS
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    More about this item

    Keywords

    option pricing; inflation-indexed mortgages; default option; explicit finite difference method; wage-indexed payment mortgage (WIPM);
    All these keywords.

    JEL classification:

    • L85 - Industrial Organization - - Industry Studies: Services - - - Real Estate Services

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