Extreme market risk and extreme value theory

The phenomenon of the occurrence of rare yet extreme events, “Black Swans” in Taleb's terminology, seems to be more apparent in financial markets around the globe. This means there is not only a need to design proper risk modelling techniques which can predict the probability of risky events in normal market conditions but also a requirement for tools which can assess the probabilities of rare financial events; like the recent global financial crisis (2007–2008). An obvious candidate, when dealing with extreme financial events and the quantification of extreme market risk is extreme value theory (EVT). This proves to be a natural statistical modelling technique of relevance. Extreme value theory provides well-established statistical models for the computation of extreme risk measures like the return level, value at risk and expected shortfall. In this paper we apply univariate extreme value theory to model extreme market risk for the ASX-All Ordinaries (Australian) index and the S&P-500 (USA) Index. We demonstrate that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or expected shortfall (ES) and expected return level and also daily VaR using a GARCH(1,1) and EVT based dynamic approach.