VaR for U.S. and european stock indices
KeywordsValue at Risk ; Historical simulation ; Variance - Covariance ; EWMA ; GARCH ; EGARCH ; Backtesting
The objective of this study is to determine the best Value-at-Risk (VaR) model for the biggest stock exchange indexes in the U.S. and Europe. We use the Historic Simulation and Variance-Covariance approach with estimated volatility from Moving Average, Exponentially Weighted Moving Average, GARCH (1,1) with Normal Distribution, GARCH (1,1) with Student-t Distribution, EGARCH (1,1) with Normal Distribution and EGARCH (1,1) with Student-t Distribution. We use these methods in order to obtain the VaR forecasts for the period 01/01/2007 to 26/09/2016 for the following indices: S&P500, NASDAQ, EUROSTOXX, FTSE100, DAX, CAC and ATHEX. For the backtesting we apply the three tests proposed by Christoffersen (2012). Our results show that the most accurate results are achieved when using the Student t distribution together with a volatility forecasting model that takes into account the leverage effect, as the EGARCH (1,1).