Application of the Gumbel Copula for Economic Risk Aggregation - a case of Kenyan Banks

Abstract

Commercial banks are some of the most heavily regulated institutions, not only in Kenya but also in other parts of the world. Increasingly, the Basel Accords have been revised to require banks to set aside enough funds to cover their risks. Commercial banks, however, face many risks chief among them market and credit risks. These risks tend to have different distributions which complicates the calculation of a firm-wide measure of risk to calculate economic capital. Many companies use value at risk as it is simple and easy to explain. However, value at risk is not wholly dependable due to the limitations associated with correlations and the fact that it does not fulfill the sub-additive property. The copula function was therefore developed to deal with these challenges. This study applies the Gumbel copula in measuring dependence and economic capital using data from Kenyan banks.