Credit Risk: From Transaction to Portfolio Management

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

tranches.

The last investment grade asset is the shorter dated maturity annu-

ity; this has a smaller monthly ‘coupon’.

References

Masters et al., The JP Morgan Guide to Credit Derivatives, Risk Metrics Group.

O’Kane, Credit Derivatives Explained, Lehman Brothers.

Discount factor

1

1 risk free rate spread





[]

t

.

Present value cashflow discount factor

1







ii

i

iN

.

∑

Securitization 217

Figure 4.31 A typical term structure.

0

2

4

6

8

1 6 11 16 21

Maturity (years)

Rate (%)

Rate

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