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).