Risk management is specially concerned with catastrophic events such as market crashes, collapses of the bond market or foreign exchange crises. Risk management tools such as value at risk models have been developed both by professionals and academics to evaluate the risk of market positions. As most of VaR models consider "normal" market conditions, they are completed by stress testing studies focusing on catastrophic events. This paper proposes a rigorous method based on the extreme value theory to define catastrophe scenarios used in stress testing methods. The stress value for a risk factor is computed for a given probability level, and inversely, a probability level is computed for a given stress value. An application is provided for foreign exchange markets.
LONGIN, F. (2001). Measuring Extreme Movements in Foreign Exchange Markets: Application of Extreme Value Theory to Stress Testing. In: Global Financial Markets at the Turn of the Century. 1st ed. Pergamon, pp. 310-320.