Semi-analytical MBS Pricing

Semi-analytical MBS Pricing 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Real Estate Finance and Economics Springer Journals
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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2007 by Springer Science+Business Media, LLC
Subject
Economics; Regional/Spatial Science; Financial Services
ISSN
0895-5638
eISSN
1573-045X
D.O.I.
10.1007/s11146-007-9020-3
Publisher site
See Article on Publisher Site

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.

Journal

The Journal of Real Estate Finance and EconomicsSpringer Journals

Published: Mar 8, 2007

References

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