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Semi-analytical MBS Pricing

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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.

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Authors and Affiliations

  1. Danske Bank Quantitative Research, Copenhagen, Denmark

    Niels Rom-Poulsen

  2. Copenhagen Business School, Frederiksberg, Denmark

    Niels Rom-Poulsen

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  1. Niels Rom-Poulsen
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Correspondence to Niels Rom-Poulsen.

Additional information

I am grateful to Leif Dydensborg, Brian Huge, Lars Peter Lilleøre, Allan Mortensen, Carsten Sørensen and two anonymous referees for helpful comments. All errors are of course my own.

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Rom-Poulsen, N. Semi-analytical MBS Pricing. J Real Estate Finan Econ 34, 463–498 (2007). https://doi.org/10.1007/s11146-007-9020-3

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  • DOI: https://doi.org/10.1007/s11146-007-9020-3

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