With the increasing level of volatility in the crude oil market, the transient data feature becomes more prevalent in the market and is no longer ignorable during the risk measurement process. Since there are multiple representations for these transient data features using a set of bases available, the sparsity measure based Morphological Component Analysis (MCA) model is proposed in this paper to find the optimal combinations of representations to model these transient data features. Therefore, this paper proposes a MCA based hybrid methodology for analyzing and forecasting the risk evolution in the crude oil market. The underlying transient data components with distinct behaviors are extracted and analyzed using MCA model. The proposed algorithm incorporates these transient data features to adjust for conservative risk estimates from traditional approach based on normal market condition during its risk measurement process. The reliability and stability of Value at Risk (VaR) estimated improve as a result of finer modeling procedure in the multi frequency and time domain while maintaining competent accuracy level, as supported by empirical studies in the representative West Taxes Intermediate (WTI) and Brent crude oil market.