The Calculation of Minimum Regulatory Capital using Single-Loss Approximations

Matthias Degen

Abstract

ABSTRACT

The calculation of the minimum regulatory capital that a financial institution needs to hold as a buffer to safeguard against adverse business outcomes is a delicate statistical issue. In this paper we highlight problems that may arise and voice a warning against a naive use of mathematical tools. Our focus is on the so-called single-loss approximation used in the operational risk industry for the calculation of minimum regulatory capital. We provide an analytical framework to study the accuracy of this approximation and, as a result, derive an improved method for the calculation of minimum regulatory capital charges. It is not the aim of our paper to advocate the use of such single-loss approximations. Rather, our contribution should be seen as an analytical justification of the essentially empirical findings of a 2006 paper by Böcker and Sprittulla.