Monte Carlo Simulation Accuracy in Estimating Value-at-Risk : Analyzing Performance Before, During and after the Financial Crisis

This paper presents an estimation of Value at Risk (VaR) using Monte Carlo Simulation (MCS) under the symmetric GARCH (1,1) model in three different markets, United States, Eurozone and Japan, represented by the indexes Dow Jones Industrial Average, Euro Stoxx 50 and Nikkei 225 respectively, before, during and after the financial crisis of 2008. The MCS is applied under the GARCH (1,1) volatility model with normal and standardized Student-t distribution of residuals (in this last case, using two different approaches to obtain the degree of freedom). Moreover, the corresponding results are analyzed and different backtesting tests as well as distance measures are employed to evaluate the performance of each model. The results show that the Monte Carlo Simulation under GARCH (1,1)-Student-t model outperforms the simulation under GARCH (1,1)-normal model especially at the level of tails, while the GARCH-normal model proved to be less overestimating VaR throughout the intervals of the study where returns were not extremely low. Finally, this work focuses on the importance of the method used to obtain the degree of freedom parameter of the Student-t distribution as it affects the quality of the VaR estimates. The main contribution of this paper is that it provides a useful analysis on VaR estimates obtained under MCS when used with GARCH family models and revealing which models might be appealing for managers and practitioners as well as regulators. Consequently, the results provided in this paper are interesting for researchers, managers and regulators to observe the behavior of the employed models and choose the model that suits their employed policies and managing the risk exposure