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# 10.1 Default Probability and Recovery Rates

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.

## 10.1.1 Defining Default Probability

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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