• Gram–Charlier expansion
• intra-day data
• realized volatility
• RGARCHRSRK
• robust skewness-kurtosis
• value at risk.

Past financial crises show the importance of adequate risk measurement techniques which adapt more rapidly to changing market circumstances. One traditional risk method is the conditional Value at Risk (VaR) using GARCH models based on low-frequency daily data. After these initial GARCH models, other models like a realized GARCH by Hansen, Huang and Lunde (2011) incorporated intra-day data, and it has become a rapid growing field in financial econometrics; but these methodologies only consider the second moment of a log-returns distribution; Previously, some researchers had started to incorporate higher moments into their GARCH models to reach a more accurate measure of VaR. Leon, Rubio, and Serna (2005) created a daily GARCH model with conditional counterparts of the sample skewness and kurtosis. In their model the standard measures of skewness and kurtosis are essentially based on averages and it can be sensitive to outliers.
Then, robust measures of third and fourth moments, proposed by Kim and White (2004), are based on quantiles rather than averages; from these developments we have calculated the RGARCHRSRK model with robust measures of skewness and kurtosis in two steps: 1) The first step is the RGARCHSK model as a mix between RGARCH Hansen et.al (2011) and GARCHSK Leon et al. (2005) models and 2) the second is the RGARCHRSRK model that uses robust measures of skewness and kurtosis in conditional higher moment equations. For both models we applied a quasi-maximum likelihood estimation with modified Gram-Charlier expansion of standardized innovations using one minute intra-day information from log-returns of S&P500 index.
Finally, we calculated and tested the accuracy of daily VaR´s using the normal distribution for GARCH(1,1) and RGARCH(1,1) and Cornish-Fisher expansion for GARCHSK(1,1,1,1), RGARCHSK(1,1,1,1) and RGARCHRSRK(1,1,1,1) models. Based on this empirical analysis, we found that the use of RGARCHRSRK(1,1,1,1) model improves the conditional VaR accuracy.