Suppose an institution has an exposure to counterparty A and insures that exposure through counterparty X (as in the case of a CCDS discussed in Section 10.2.5). The institution now has a (reduced) risk, as it is only exposure in the case of counterparties A and X both defaulting. Let us consider four possible outcomes, as illustrated in Figure 11.1. We need to consider the following relationships between entities A and X:

*Mutually exclusive*. Mutually exclusive events cannot occur at the same time. For default events to be mutually exclusive there would have to be negative correlation between them. This is unlikely to be the case for defaults, except in rare circumstances where two competitors may be considered unlikely to default together since the failure of one would give the other an increased market share.^{1}*Independent*. Independent events happen with no underlying linkage so that occurrence of one event makes it neither more nor less probable that the other event occurs. When throwing two coins, the outcomes are independent. Independent events can happen together (circles overlapping), although ...

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