The calculation of capital requirement using Extreme Value Theory

The Basel Committee has suggested some formulas for calculating capital requirement using the Advanced Internal Ratings-Based Approach. However, these formulas were derived under the assumption of a normal distribution. Thus, the capital requirement estimated by the Basel formula may be incorrect when the asset distributions are not normal. Using an analysis of qualifying revolving retail exposures as an example, this paper introduces a formula based on the Extreme Value Theory to calculate the capital requirement. This formula is more general and accurate than its predecessors, because it can be used with any type of distribution. Numerical examples are provided to demonstrate that the capital requirement estimated by the Basel formula is less than by our formula when the asset distribution has a heavy tail, and more than by our formula when the distribution has a short tail. Our formula is also more sensitive to risk than competing models in the context of the recent financial crisis.