Alternative modeling for long term risk

In this paper, we propose an alternative approach to estimate long-term risk. Instead of using the static square root of time method, we use a dynamic approach based on volatility forecasting by non-linear models. We explore the possibility of improving the estimations using different models and distributions. By comparing the estimations of two risk measures, value at risk and expected shortfall, with different models and innovations at short-, median- and long-term horizon, we find that the best model varies with the forecasting horizon and that the generalized Pareto distribution gives the most conservative estimations with all the models at all the horizons. The empirical results show that the square root method underestimates risk at long horizons and our approach is more competitive for risk estimation over a long term.