Value at Risk, Expected Shortfall, and Marginal Risk Contributions

Value at risk (VaR) is today the standard tool in risk management for banks and other financial institutions. It is defined as the worst loss for a given confidence level: For a confidence level of e.g. p=99%, one is 99% certain that at the end of a chosen risk horizon there will be no greater loss than just the VaR. In terms of probability theory, VaR is the 1% quantile (in general the (1-p)% quantile) of the profit and loss distribution.

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Alternative title:	Value at Risk, erwartetes Defizit und Grenzrisiko-Beiträge
Year of publication:	2002-05-01
Authors:	Rau-Bredow, Hans
Published in:	Universität Würzburg - Lehrstuhl für Betriebswirtschaftslehre, Bank- und Kreditwirtschaft - Publikationen G. Szego (Ed.): New Risk Measures in Investment and Regulation, Wiley, 2004
Publisher:	Institut für Bank- und Kreditwirtschaft <Würzburg>
Subject:	Kreditwesen \| Bank \| Value at Risk \| Ausfallrisiko \| Kreditrisiko

1. Introduction
2. Value at Risk as a problematic risk measure
3. Derivatives of Value at Risk and Expected Shortfall
3.1 Preliminary remarks
3.2 First and second derivative of Value at Risk
3.3 First and second derivative of Expected Shortfall
4. Outlook

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