Oil price markets can benefit from a better considerate of how shocks can affect volatility through time. This study assesses the impact of structural changes and outliers on volatility persistence of two crude oil markets WTI and Brent oil price between January 1, 1996 and March 17, 2014. First, we identify the FIGARCH process proposed by Baillie et al. (1996) [Baillie, R.T., Bollerslev, T., & Mikkelsen, H.O., (1996), Fractionally integrated generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 74, 3-30.] and investigate some of its statistical proprieties and then incorporate this information into the volatility modelling. We also show that outliers can bias the estimation of the persistence of the volatility. Taking into account outliers on the volatility modelling process improve the understanding of volatility in crude oil markets.