Forecasting VaR and ES of stock index portfolio: A Vine copula method

Abstract

Risk measurement has both theoretical and practical significance in risk management. Using daily sample of 10 international stock indices, firstly this paper models the internal structures among different stock markets with C-Vine, D-Vine and R-Vine copula models. Secondly, the Value-at-Risk (VaR) and Expected Shortfall (ES) of the international stock markets portfolio are forecasted using Monte Carlo method based on the estimated dependence of different Vine copulas. Finally, the accuracy of VaR and ES measurements obtained from different statistical models are evaluated by UC, IND, CC and Posterior analysis. The empirical results show that the VaR forecasts at the quantile levels of 0.9, 0.95, 0.975 and 0.99 with three kinds of Vine copula models are sufficiently accurate. Several traditional methods, such as historical simulation, mean-variance and DCC-GARCH models, fail to pass the CC backtesting. The Vine copula methods can accurately forecast the ES of the portfolio on the base of VaR measurement, and D-Vine copula model is superior to other Vine copulas.