In this release of SPV the focus has been on valuation of MBBs.
Specifically the following two subjects have been treated.
- A simple specification of the delivery option.
- A model with a state dependent option adjusted spread.
The simple specification of the delivery option is based on an estimated
relationship between the present value of the loan and the observed market
price.
This relationship is then used throughout the binomial trees of the
respective loan groups to determine if the delivery option is exercised, solving a technical problem present in other methods
where the decision to exercise the delivery option is based on the theoretical
value of the bond which is different in the respective loan groups.
We find that for bonds with a long maturity there is virtually no difference
between this and alternative methods while for bonds of shorter maturity this
simple specification produces OA values which are consistently higher than the
OA values produced with other versions of the delivery option.
The state dependent OA spread should be seen as a first attempt to avoid the
static OA spread which is added to all nodes in all binomial trees of the
respective loan groups. The approach is very simple. In a given node the OA
convexity is calculated based on the theoretical values of the bond in
neighbouring states. If the convexity is negative a spread is added along with a
constant value, a, the more
negative convexity the higher the added spread. This sensitivity is controlled
by a b parameter. If the convexity is positive only
the constant spread is added.
The two parameters are then calibrated to fit theoretical values to observed
market prices on a given day. As desired we find that negative convexity is
'punished' by an increased spread.
Afterwards the parameters are used to calculate OA values and sensitivity
measures at future dates.
This approach is very similar to what is termed the PPRisk measure, however,
this method is much faster in term of calculation speed given that only a single backward run through the binomial
tree is required.