This article focuses on the application of the Pykhtin model to the Italian banking system to measure concentration risk by industry sector and geographic region. The proposed approach generalizes the portfolio model used in Pillar 1 for the calculation of the capital requirement, removing the assumptions of the existence of one systematic risk factor and of an infinitely granular portfolio.
The difference between the unexpected loss stemming from the Pykhtin model and that calculated using the supervisory formula can be interpreted as a measure of concentration risk. The Pykhtin model is consistent with the Basel II framework. It accordingly generates an unexpected loss measure that is in line with the IRB capital requirements. The proposed model therefore has the advantage of "speaking the language of supervisors". This approach makes it possible to interpret the difference between regulatory and economic capital.
It also enables concentration risk to be broken down into its two components: single-name and sectoral/geographic concentration risk. The empirical results show the model's ability to generate internally coherent rankings that are close to the economic intuition: exposure to sectoral/geographic concentration risk is negatively correlated to banks'size.
