For n = 50, each position has a future value, if it doesn’t default, of $2,000,000. The expected loss is $2,000,000 (total portfolio value times the probability of default = 0.02 × 100,000,000) which is the same as for a single-credit portfolio. If there are three defaults, the credit loss is $6,000,000 (= 3 × $2000,000). The credit VaR at the 95% confidence level is $4,000,000 (credit loss of $6,000,000 less the expected loss of $2,000,000)

Note that in this case, we assume that the recovery rate is zero, so LGD is 1.

Things to Remember

• Default correlation: Default correlation measures the degree to which the defaults of different credits are related. It is an important concept in credit risk modeling.
• Binomial distribution: In credit risk modeling, the binomial distribution is often used to model the number of defaults in a portfolio. It is a discrete probability distribution that describes the number of successes in a fixed number of trials.
• Credit Value at Risk (VaR): Credit VaR is a measure of potential loss in a credit portfolio due to defaults. It helps in quantifying the risk of loss in a credit portfolio at a certain confidence level over a specified time horizon.
• Expected loss: Expected loss is the average loss that can be expected in a credit portfolio over a specified period. It is calculated as the product of the exposure at