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Valuation of Mortgage-Backed Securities and Mortgage Derivatives: A Closed-Form Approximation

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  • Andreas Kolbe
  • Rudi Zagst

Abstract

In this paper we develop a closed-form and thus computationally highly efficient formula to approximate the value of fixed-rate mortgage-backed securities (MBS). Our modelling framework is based on reduced-form and prepayment-risk-neutral valuation techniques and offers two major extensions compared with existing closed-form approximation approaches: we include a stochastic baseline prepayment factor in our model and we are able to capture the usual S-shaped curve of the refinancing incentive by a piecewise linear approximation. We apply our model to GNMA pass-through securities and test it on a 10-year sample of monthly GNMA MBS market prices for a wide range of coupons.

Suggested Citation

  • Andreas Kolbe & Rudi Zagst, 2009. "Valuation of Mortgage-Backed Securities and Mortgage Derivatives: A Closed-Form Approximation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(5), pages 401-427.
  • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:5:p:401-427
    DOI: 10.1080/13504860902781419
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