To value any cash ﬂow stream then we use the equation below:
Here we multiply each cash ﬂow occurring at time t with the discount
factor at the corresponding time. These individual components are then
summed up. The only further piece of information required is the rele-
vant term structure to obtain the discount factor. This is determined
from a combination of the risk free rate and a correction which allows
for a possible default on the obligor. This default is assessed by the mar-
ket and added to the risk free rate in the form of a spread. (The spread
can have maturity dependence.) The discount factor thus has the form:
The spread accorded to the obligor not surprisingly depends on the
credit rating assigned to the borrower. We have three investment grade
tranches, this means that spread over the risk free rate will be quite
small because of the low likelihood of default. Figure 4.31 shows the
pricing curve or term structure used to obtain the value of the senior
The last investment grade asset is the shorter dated maturity annu-
ity; this has a smaller monthly ‘coupon’.
Masters et al., The JP Morgan Guide to Credit Derivatives, Risk Metrics Group.
O’Kane, Credit Derivatives Explained, Lehman Brothers.
1 risk free rate spread
Present value cashflow discount factor
Figure 4.31 A typical term structure.
1 6 11 16 21