We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We present a simulated study regarding the estimation of the risk measure VaRp on FIEGARCH processes. We consider the distribution function of the portfolio log-returns (univariate case) and the multivariate distribution function of the risk-factor changes (multivariate case). We also compare the performance of the risk measures VaRp, ESp and MaxLoss for a portfolio composed by stocks of four Brazilian companies.