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Question 26.5: Suppose that the credit loss in a year has a lognormal distr...

Suppose that the credit loss in a year has a lognormal distribution. The logarithm of the loss is normal with mean 0.5 and standard deviation 4. What is the economic capital requirement if a confidence level of 99.97% is used?

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The 99.97% worst-case value of the logarithm of the loss is 0.5 + 4 × 3.43 = 14.23.The 99.97% worst-case loss is therefore $1.510 million. From the properties of the lognormal distribution, the expected loss is exp(0.5 + 4²/2) or $4,915. The capital requirement is therefore $1.505 million.

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