A threshold based approach to merge data in financial risk management

Abstract

According to the last proposals by the Basel Committee, banks are allowed to use statistical approaches for the computation of their capital charge covering financial risks such as credit risk, market risk and operational risk.

It is widely recognized that internal loss data alone do not suffice to provide accurate capital charge in financial risk management, especially for high-severity and low-frequency events. Financial institutions typically use external loss data to augment the available evidence and, therefore, provide more accurate risk estimates. Rigorous statistical treatments are required to make internal and external data comparable and to ensure that merging the two databases leads to unbiased estimates.

The goal of this paper is to propose a correct statistical treatment to make the external and internal data comparable and, therefore, mergeable. Such methodology augments internal losses with relevant, rather than redundant, external loss data.

Keywords:

• data merging
• threshold
• financial risk management

Acknowledgements

This work has been supported by MUSING 2006 (contract number 027097), 2006–2010 and Firb 2006–2009. We thank the referees for their useful comments and suggestions. This paper is the result of a close collaboration among the authors. However, Sections 1, 2 and 5 have been written by Silvia Figini, Section 3 has been written by Pierpaolo Uberti, and Section 4 has been written by Silvia Figini and Pierpaolo Uberti.

Notes

A real function f defined on the convex set is said quasi-convex if and , then