Tail Risk Research Based On Conditional Extreme Value Model

The outbreak of Global Financial Crisis in2008has sparked people’s great attention to market extreme risk. As modern financial tail risk measure, Value-at-Risk(VaR) and Expected Shortfall(ES) get widely used in industry. For asset management companies, hedge fund, investment banks, commercial banks and many individual investors, it is extremely important to predict market tail risk effectively.Auto Regressive Moving Average Generalized Auto Regressive Conditional Heteroskedastic(ARMA-GARCH) model can capture time-varying structures of both mean and volatility. In classical univariate Extreme Value Theory(EVT), Peak-over-Threshold(POT) model can fit the tail part of random variables with independent identical distribution precisely. If we combine these two models, we obtain conditional EVT model, which could make use of advantages of both models to become the powerful tool for describe the dynamic tail properties of return series.This paper uses three different kinds of ARMA-GARCH model(each model has different assumption for distribution of innovation) and three corresponding conditional EVT models, perform two-side VaR and ES prediction and out-of-sample back testing under significance levels of95%,99%and99.5%for five market indexes from China, USA, Europe, Japan and India around the recent decade. The results show that since ARMA-GARCH model with normal innovation could not capture the asymmetric and heavily-tailed properties, it could not predict VaR and ES precisely, especially under the condition of high significance. Since ARMA-GARCH model with student/innovation could not describe the asymmetric property, the results could not be improved as well. However, the adoption of skewed t innovation makes great progress in predicting the two measures. For the above three ARMA-GARCH models, if we use Peak-over-Threshold(POT) model instead of raw parametric model to estimate the tail part of innovation, no matter which kind of distribution we use for innovation, the results of back testing are excellent. The paper has performed some research in predicting and control market tail risk scientifically for risk management industry of our country, and provided reliable technical materials of learning market extreme risk for many financial institutions and individual investors.