Comparing Value-at-Risk Methodologies

We perform a Monte Carlo experimet to compare four different Value-at-Risk methodologies, RiskMetrics, Gaussian GARCH(1,1), Generalized Student-t APARCH(1,1), and ARCH(1) Quantile, under five different data generating processes. The ARCH(1) Quantile methodology does not assume any distribution for the returns, and this robustness is shown to avoid trajectories with too many violations. The number of violations tends to be higher in the non-robust methodologies when the distribution differs from the Gaussian one. We also perform an empirical exercise applying the four Value-at-Risk methodologies to daily return of the IBOVESPA (measured in dollar values) in a period of market turmoil (1996-2000), when happens the Korean crisis, the Russian crisis and the blast of the technology-stock market bubble. We display that, again, the ARCH(1) Quantile methodology dominates the non-robust methodologies, in the sense that it presents the least number of violations