In Chapter 9, we have discussed in detail how to quantify exposure, which covers the EE term in equation (12.2). Institutions may commonly take EE values from a risk management system, even though that system may have been set up for monitoring credit lines and not computing CVA. However, there is one caveat. For quantifying exposure for risk management, as discussed in Section 9.4.1, one should use the real probability measure whereas for pricing purposes the risk-neutral measure should be used. The use of the risk-neutral versus real probability measure is an important point and hence will be discussed in more detail in Chapter 16. We now discuss some aspects of exposure, not covered in Chapter 9, which relate to the potential need to calculate risk-neutral exposure for CVA purposes.

In the above, we consider a separate discount factor in order to discount future losses to today, and arrive at a price (the CVA). It is reasonable to do this as long as the exposure is calculated in the correct fashion. A problem could arise, for example, in an interest rate product where, when rates are high a larger discount factor should be used, and vice versa. This convexity effect would mean that we would overestimate the CVA of a payer swap and vice versa for a receiver swap.^{9} To solve this problem technically means quantifying the underlying exposure using the “T-forward measure” (Jamshidian, 1997). By doing this, discount factors depend ...

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