| 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 tn
can be found by computing two expectations of the pool size at time t n-1 and tn respectively.
This is a general results 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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