Extreme Value at Risk and Expected Shortfall During Financial Crisis
19 Pages Posted: 21 Jan 2011
Date Written: June 20, 2010
Abstract
This paper presents Peak Over Threshold’s method and the generalized Pareto distribution of extreme value theory to measure Value at Risk and Expected Shortfall for CAC 40 and S&P 500 indexes during the 2008 financial crisis. We consider 1 day, 5 days and 10 days time horizons. The results of extreme value theory model are compared with those of traditional historical simulation through backtesting process on 250 days. We show an underestimation of the risk of loss for VaR models. This underestimation is stronger for the historical VaR model than that extreme values theory VaR model. The backtesting process also indicates a certain reliability of the measure of Expected Shorfall based on the extreme value theory. For the studied assets with some of the numerous authorized calculations, the Basell II agreement appears to be a good supervision. In fact, concerning the capital requirement for banks, all measures, even in the deeper of the crisis, lead to a sufficient cushion of capital.
Keywords: Market risk, Value at Risk, Extreme Value Theory, Risk Measurement, Risk Management, Financial Crisis
JEL Classification: G21,G33,G18
Suggested Citation: Suggested Citation
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