Estimation of multi-period VaR based on the simulation and parametric methods

Abstract: With regard to the Basel Committee’s emphasis on the necessity of using 10-day Value-at-Risk (VaR) internal models in order to determine minimum market risk capital requirements, and downsides of the square-root-of-time rule, our purpose is to produce more accurate forecasts of the multi-period VaR using sixteen models for three stock indices, the TEPIX, NASDAQ, and FTSE. The results, based on the sum of the loss function and efficiency criteria indicate that the bootstrapped historical simulation (BHS) model performs the best for the TEPIX. Also, at the 95% confidence level the parametric EGARCH model with the Student’s t innovation and at the 99% and 99.5% confidence levels the EGARCH model with the normal innovation clearly outperform other models in estimating the 5-day VaR for both the NASDAQ and FTSE indices. In addition, our findings indicate that the best model based on the conditional coverage test is not necessarily the most economical model in estimating the 5-day VaR.