Chapter 7: Common Contracts 315
Collateralized Debt Obligation (CDO) is a pool of debt instru-
ments securitized into one financial instrument. The pool
may consist of hundreds of individual debt instruments.
They are exposed to credit risk, as well as interest risk,
of the underlying instruments. CDOs are issued in several
tranches which divide up the pool of debt into instruments
with varying degrees of exposure to credit risk. One can buy
different tranches so as to gain exposure to different levels of
loss.
The aggregate loss is the sum of all losses due to default. As
more and more companies default so the aggregate loss will
increase. The tranches are specified by levels, as percentages
of notional. For example, there may be the 0–3% tranche, and
the 3–7% tranche etc. As the aggregate loss increases past
each of the 3%, 7%, etc. hurdles so the owner of that tranche
will begin to receive compensation, at the same rate as the
losses are piling up. You will only be compensated once your
attachment point has been reached, and until the detachment
point. The pricing of these contracts requires a model for the
relationship between the defaults in each of the underlying
instruments. A common approach is to use copulas. However,
because of the potentially large number of parameters needed
to represent the relationship between underlyings, the corre-
lations, it is also common to make simplifying assumptions.
Such simplifications might be to assume a single common
random factor representing default, and a single parameter
representing all correlations.
Collateralized Debt Obligation Squared (CDO^2 ) is a CDO-like con-
tract in which the underlyings are other CDOs instead of being
the simpler risky bonds.
Collateralized Mortgage Obligation (CMO) is a pool of mortgages
securitized into one financial instrument. As with CDOs there
are different tranches allowing investors to participate in dif-
ferent parts of the cashflows. The cashflows in a mortgage
are interest and principal, and the CMOs may participate in
either or both of these depending on the structure. The dif-
ferent tranches may correspond to different maturities of the
underlying mortgages, for example. The risk associated with