An application of value at risk and expected shortfall

Abstract

The last two decades have been characterized by significant volatilities in financial world marked by few major crises, market crashes and bankruptcies of large corporations and liquidations of major financial institutions. In this context, this study considers the Extreme Value Theory (EVT), which provides well established statistical models for the computation of extreme risk measures like the Value at Risk (VaR) and Expected Shortfall (ES) and examines how EVT can be used to model tail risk measures and related confidence interval, applying it to daily log-returns on four market indices. These market indices represent the countries with greater commercial trade with Brazil for last decade (China, U.S. and Argentina). We calculate the daily VaR and ES for the returns of IBOV, SPX, SHCOMP and MERVAL stock markets from January 2nd 2004 to September 8th 2014, combining the EVT with GARCH models. Results show that EVT can be useful for assessing the size of extreme events and that it can be applied to financial market return series. We also verified that MERVAL is the stock market that is most exposed to extreme losses, followed by the IBOV. The least exposed to daily extreme variations are SPX and SHCOMP.