have a large demand for long dated constant payment. This is because
policy holders at some point convert their investment into a stream of
annuity payments.
The redemption schedule from 2018 until 2023 is trickier, and we
need to appeal to the concept of amortization and zero coupon. These
are intimidating sound phrases but the underlying ideas are straight-
forward. A good example is provided by an interest and principal mort-
gage. Here the monthly payment to the lender consists of both interest
on the underlying loan and a contribution to pay off some of the out-
standing capital. The underlying loan would be said to be amortized
over the lifetime of the mortgage. There is no need however for the loan
to be paid according to this schedule however and many different
structures exist within the capital markets.
A zero coupon structure is simply a bond that pays out no interest.
How can this have any appeal? Well, the interest is embedded so
to speak in the terms of the bond. They are always offered at a dis-
count to the nominal. The discount is such that over the lifetime of the
zero the difference in value between the cost and the redemption
at par gives a return comparable to other bonds having the same
maturity.
Back to the structure then. We can anticipate the need for some
kind of amortization simply with recourse to the downward sloping
loan profile, this requires the payoff of principal to begin in 2018 and
end in 2023 or thereabouts. The demand for zeros comes from both
banks and insurance companies; they are flexible instruments which
can be used for interest rate hedging. The two instruments described
so far constitute the investment grade portion of the structure. The
bank wishing to free capital from its balance sheet wishes to obtain a
high price as possible. How are they valued?
Valuation of the investment grade assets
To properly value any fixed-income instrument you require something
called the ‘zero coupon curve’. This is none other than the time value
of money. If I lent out some money I would expect a higher rate of
return the longer the lending period to compensate me for the inabil-
ity to profit from any changes in the shorter term rate. This plot of
interest rate against maturity goes by the rather intimidating name of
a ‘term structure’. Once I have this plot I can use it to exactly discount
cash flows to determine how much they are worth today. It is a
marvellous device; it enables a comparison of payments occurring at
different times. Figure 4.31 shows a typical plot.
216 Credit risk: from transaction to portfolio management

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