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UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation

Author

Listed:
  • José A. Azevedo‐Pereira
  • David P. Newton
  • Dean A. Paxson

Abstract

We use a mean‐reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lender’s coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed‐form solution, an explicit finite difference method is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lender’s (residual) exposure to house price risk, given the borrower’s options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:reesec:v:30:y:2002:i:2:p:185-211
    DOI: 10.1111/1540-6229.00037
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    Citations

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    Cited by:

    1. 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.
    2. repec:vuw:vuwscr:19215 is not listed on IDEAS
    3. Ming Shann Tsai & Shu Ling Chiang, 2015. "A General Pricing Model for a Mortgage Insurance Contract Considering the Effects of Multivariate Random Variables on Termination Probabilities and Loss Rate," Housing Policy Debate, Taylor & Francis Journals, vol. 25(2), pages 289-307, April.
    4. Sanders, Anthony B. & Slawson, V. Jr., 2005. "Shared appreciation mortgages: Lessons from the UK," Journal of Housing Economics, Elsevier, vol. 14(3), pages 178-193, September.
    5. 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.
    6. Cristina Viegas & Jos� Azevedo-Pereira, 2012. "Mortgage valuation: a quasi-closed-form solution," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 993-1001, May.
    7. Patel, Nimesh & Daglish, Toby, 2011. "Fixed come hell or high water? Selection and prepayment of fixed rate mortgages outside the US," Working Paper Series 4107, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    8. Chang-Chih Chen & Chia-Chien Chang, 2019. "How Big are the Ambiguity-Based Premiums on Mortgage Insurances?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(1), pages 133-157, January.
    9. Calvo-Garrido, María del Carmen & Vázquez, Carlos, 2015. "Effects of jump-diffusion models for the house price dynamics in the pricing of fixed-rate mortgages, insurance and coinsurance," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 730-742.
    10. Sanders, Anthony B. & Slawson, V. Carlos, Jr., 2005. "Shared Appreciation Mortgages: Lessons from the UK," Working Paper Series 2005-16, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    11. Nicholas Sharp & Paul Johnson & David Newton & Peter Duck, 2009. "A New Prepayment Model (with Default): An Occupation-time Derivative Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 39(2), pages 118-145, August.
    12. Lanot, Gauthier & Leece, David, 2010. "The Performance of UK Securitized Subprime Mortgage Debt: ‘Idiosyncratic’ Behaviour or Mortgage Design?," MPRA Paper 27137, University Library of Munich, Germany.

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