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

Posted: 20 Oct 2007 Last revised: 15 Jul 2008

See all articles by Nick J. Sharp

Nick J. Sharp

Nottingham University Business School (NUBS)

Peter Duck

University of Manchester - Department of Mathematics

David Newton

University of Bath - School of Management

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

Suggested Citation

Sharp, Nick J. and Duck, Peter and Newton, David, An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options. Journal of Real Estate Finance and Economics, Vol. 36, No. 3, 2008, Available at SSRN: https://ssrn.com/abstract=1022986

Nick J. Sharp

Nottingham University Business School (NUBS) ( email )

Jubilee Campus
Wollaton Road
Nottingham, NG8 1BB
United Kingdom
+441519515258 (Phone)

Peter Duck (Contact Author)

University of Manchester - Department of Mathematics ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

David Newton

University of Bath - School of Management ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

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