## Expected and Worst Exposure

The expected credit exposure (ECE) is the expected value of the asset replacement value x, if positive, on a target date:

Expected Credit Exposure =

The worst credit exposure (WCE) is the largest (worst) credit exposure at some level of confidence. defined as Credit at Risk (CAR). It is implicitly defined as the value such that it is not exceeded at the given confidence level p:

To model the potential credit exposure, we need to (i) model the distribution of risk factors, and (ii) evaluate the instrument given these risk factors. This process is identical to a market value-at-risk (VAR) computation except that the aggregation takes place first at the counterparty level and second at the portfolio level.

To simplify to the extreme, suppose that the payoff x is normally distributed with mean zero and volatility a. The expected credit exposure is then

Note that we divided by 2 because there is a 50 percent probability that the value will be positive. The worst credit exposure at the 95 percent level is given by

Figure 21-1 illustrates the measurement of ECE and WCE for a normal distribution. Note that negative values of x are not considered.

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