Stress testing for VaR and CVaR

Abstract

The practical use of the contamination technique in stress testing for risk measures Value at Risk (VaR) and Conditional Value at Risk (CVaR) and for optimization problems with these risk criteria is discussed. Whereas for CVaR its application is straightforward, the presence of the simple chance constraint in the definition of VaR requires that various distributional and structural properties are fulfilled, namely for the unperturbed problem. These requirements rule out direct applications of the contamination technique in the case of discrete distributions, which includes the empirical VaR. On the other hand, in the case of a normal distribution and parametric VaR, one may exploit stability results valid for quadratic programs.

Keywords:

• Stochastic programming
• Risk management
• Portfolio optimization
• Linear programming
• Fixed-income markets
• Asset liability modelling
• Dynamic models

Acknowledgements

This research was supported by the project ‘Methods of modern mathematics and their applications’ (MSM 0021620839) and by the Grant Agency of the Czech Republic (grants 201/05/2340 and 402/05/0115).