An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options

  • Nicholas J. Sharp
  • David P. Newton
  • Peter W. Duck
Article
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Abstract

This paper considers in detail a realistic mortgage valuation model (including the potential for early prepayment and the risk of default), based on stochastic house-price and interest-rate models. As well as the development of a highly accurate numerical scheme to tackle the resulting partial differential equations, this paper also exploits singular perturbation theory (a mathematically rigorous procedure, based on the idea of the smallness of the volatilities), whereby mortgage valuation can be accurately approximated by very simple closed-form solutions. Determination of equilibrium contract rates, previously requiring many computational hours is reduced to just a few seconds, rendering this a highly useful portfolio management tool; these approximations compare favorably with the full numerical solutions. The method is of wide applicability in US or other mortgage markets and is demonstrated for UK fixed-rate mortgages, including insurance and coinsurance.

Keywords

Fixed-rate mortgages Option pricing theory Perturbation theory Prepayment Default 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Nicholas J. Sharp
    • 1
  • David P. Newton
    • 1
  • Peter W. Duck
    • 2
  1. 1.Nottingham University Business SchoolNottinghamUK
  2. 2.School of MathematicsThe University of ManchesterManchesterUK

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