An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariate

Prof. Dr. Paul Embrechts

ETH Zurich

About the Speaker

Paul Embrechts is Professor of Mathematics at the ETH Zurich specialising in Actuarial Mathematics and Quantitative Risk Management.

Previous academic positions include the Universities of Leuven, Limburg and London (Imperial College). Dr. Embrechts has held visiting professorships at numerous universities and has an Honorary Doctorate from the University of Waterloo, the Heriot-Watt University, Edinburgh, and the Université Catholique de Louvain. He is an Elected Fellow of the Institute of Mathematical Statistics and the American Statistical Association, Honorary Fellow of the Institute and the Faculty of Actuaries, UK, and Institut des Actuaires, France and Member Honoris Causa of the Belgian Institute of Actuaries. He belongs to various national and international research and academic advisory committees.

He co-authored the influential books "Modelling of Extremal Events for Insurance and Finance", Springer, 1997, and "Quantitative Risk Management: Concepts, Techniques and Tools", Princeton University Press, 2005 and 2015.

Dr. Embrechts consults on issues in Quantitative Risk Management for financial institutions, insurance companies and international regulatory authorities.

Abstract

In financial risk management, Operational Risk data typically appear as entries in a BLxRT-matrix where BL stands for the number of business lines, and RT corresponds to risk types. For instance (BL) Corporate Finance and (RT) Internal Fraud.

Banks and insurance companies often, at least for internal purposes, model Operational Risk losses based on such a data matrix and use a particular risk measure to be statistically estimated. From a mathematical point of view the (internal) data available consists of BLxRT marked point processes. A typical example consists of a (BL=8, RT=7)-matrix, with historical data in each cell. As risk measure one often takes a high quantile of the total matrix loss distribution function over a one year horizon (referred to in the industry as a one-year Value-at-Risk). In order to analyze this problem we introduce a dynamic version of Extreme Value Theory (EVT) introducing as co-variables rows, columns from the data matrix as well as time. The Operational Risk example is just mentioned as a motivating example, the general EVT methodology discussed is applicable well beyond this example.

This talk is based on joint work with Valerie Chavez-Demoulin (EPF Lausanne) and Marius Hofert (University of Waterloo).