İstatistik Araştırma Dergisi

Abstract

We estimate Value at Risk (VaR) using the extreme value theory. VaR is a method emerging recently in risk management. Extreme value theory models the tails of the return distribution rather than the whole distribution, which is more meaningful during the volatile market conditions, under which the distribution of returns almost has fat tail. Risk managers are more concerned on the tail. The limit distribution of extreme returns observed over a long time period is independent of the distribution of returns itself. In this case, it is not necessary to assume a specific distribution for returns, which is a great advantage of extreme value theory on VaR calculation. In contrast, variance-covarience method with normality assumption usually under estimates the risk value. The maxima and minima series from İstanbul stock Exchange index returns are found to be satisfactorily modelled within an extreme value framework and the Var measures generated with this method are found to be much different from those generated by variance-covariance method. The approach based extreme value theory to compute VaR cover market conditions ranging from usual environment considered by the ordinary VaR methods to the financial crises which are focus of stress testing. Moreover, extreme value approach can also be used to calculate credit VaR.