An example of historical default rates for investment- and speculative-grade assets is shown in Figure 10.1, illustrating that default rates tend to vary substantially through the economic cycle.

Source: Standard & Poor's (2008)

In Appendix 10A we define default probability in more mathematical detail. We refer to the cumulative default probability, , which gives the probability of default any time from now (assuming the counterparty is not currently in default) until time *t*. This is illustrated in Figure 10.2. The function must clearly start from zero and tend towards 100% (every counterparty defaults eventually!). A marginal default probability, which is then the probability of a default between two specified future dates, is given by

(10.1)

We can see that must be monotonically increasing to avoid marginal ...

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