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Semi-analytical MBS Pricing

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  • Niels Rom-Poulsen

Abstract

This paper presents a multi-factor valuation model for fixed-rate callable mortgage backed securities (MBS). The model yields semi-analytic solutions for the value of MBS in the sense that the MBS value is found by solving a system of ordinary differential equations. Instead of modelling the conditional prepayment rate (CPR), as is customary, the pool size is the primary modelling object. It is shown that the value of a single MBS payment due at time t n can be found by computing two expectations of the pool size at time t n–1 and t n respectively. This is a general result independent of any interest rate model. However, if the pool size is specified in a way that makes the expectations solvable using transform methods, semi-analytic pricing formulas are achieved. The affine and quadratic pricing frameworks are combined to get flexible and sophisticated prepayment functions. We show that the model has no problem of generating negative convexity as the spot rate falls, and still be close to a similar non-callable bond when the spot rate rises. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May.
    • Handle: RePEc:kap:jrefec:v:34:y:2007:i:4:p:463-498
    DOI: 10.1007/s11146-007-9020-3
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    References listed on IDEAS

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    Cited by:

    1. Gianluca Marcato & Giovanni Alberto Tira, 2009. "Driving Factors in Pricing European CMBS: Bond, Mortgage and Real Estate Characteristics," ERES eres2009_145, European Real Estate Society (ERES).
    2. Ahmad, F. & Hambly, B.M. & Ledger, S., 2018. "A stochastic partial differential equation model for the pricing of mortgage-backed securities," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3778-3806.
    3. Ahmad, Ferhana & Shehzad, Choudhry Tanveer, 2024. "The role of interest rate environment in mortgage pricing," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 225-245.

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