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# 15.2 Overview of Wrong-way Risk

## 15.2.1 Simple Example

Imagine tossing two coins and being asked to assess the probability of getting two heads – that is an easy question to answer.1 Now suppose that you are told that the coins are linked in some way: the first coin to land can magically have some impact on which way up the other coin lands. Clearly, the question is now much more complex.

In Chapter 12, we saw that CVA could be generally represented as credit spread multiplied by exposure. Indeed, an approximate formula for CVA was simply CVA = credit spread × EPE. However, the multiplication of the default probability (credit spread) and exposure (EPE) terms relies on a key assumption, which is that the different quantities are independent. If they are dependent then the analysis is far more complicated and the relatively simple formulas are no longer appropriate. Essentially this corresponds to the integration of credit risk (default probability) and market risk (exposure), which is a very complex task. We could have other dependence such as between loss given default (and equivalently recovery rate) and either exposure or default probability, which will also give rise to other forms of wrong-way risk.

A simple analogy to wrong-way risk is dropping (the default) a piece of buttered bread. Many people believe that in such a case, the bread is most likely to land on the wrong, buttered side (exposure). This is due to “Murphy's Law”, which states that “anything that can go wrong, ...

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