We have calculated a first year gain from prepayment, as an attempt to
capture prepayments from borrowers who focus on short term profits.
Within segments of maturities, 0-10, 10-20 and 20-30, a refinancing bond is
selected as the bond within the same range of maturity with the highest coupon
such that the difference in price is less than 3. It turns out that this very
simple rule captures the refinancing behaviour quite well, especially for short
and long loans.
With the definition of the refinancing bond in place the first year saving,
FYS, from prepayment can be calculated in a straightforward way.
The figure below shows the development in FYS (in percent) together with the
standard prepayment gain for the NYK 8'31 bond. The green series denotes the
standard prepayment gain, the blue series first year saving and the pink dots
indicate the coupon of the refinancing bond.
We see that FYS and gain variables, not suprisingly, move in the same
direction over time, and in fact it turns out that in this period the two series
have a correlation coefficient of 0.91.
A model, extending the standard DMBS model, has been estimated, incorporating
the FYS in percent as an explanatory variable. To illustrate the impact on the
parameters, two figures have been included. The figure directly below shows a
scatter plot of estimated and actual CPR from the DMBS model, that is without
FYS.
The figure below is the equivalent of the chart above, but for a model
extending the DMBS model with the FYS variable. We see that the overall fit is
virtually unchanged. However, we see that eg. for the green dots, indicating the
most recent observations, the model using the FYS variable tends to
underestimate prepayments less for observations with high actual prepayments.
For the estimated parameters we find that the FYS parameters are very often
statistically insignificant, an indication that the gain variable, combined with
the high correlation, explains the prepayments quite well, and even explains
part of the FYS.
