Herrera, R (reprint author) Univ Talca, Fac Ingn, Dept Modelac & Gest Ind, Camino Los Niches Km 1, Curico, Chile.Crude oil is a dynamically traded commodity that affects many economies. We propose a collection of marked self-exciting point processes with dependent arrival rates for extreme events in oil markets and related risk measures. The models treat the time among extreme events in oil markets as a stochastic process. The main advantage of this approach is its capability to capture the short, medium and long-term behavior of extremes without involving an arbitrary stochastic volatility model or a prefiltration of the data, as is common in extreme value theory applications. We make use of the proposed model in order to obtain an improved estimate for the Value at Risk in oil markets. Empirical findings suggest that the reliability and stability of Value at Risk estimates improve as a result of finer modeling approach. This is supported by an empirical application in the representative West Texas Intermediate (WTI) and Brent crude oil markets. (C) 2013 Elsevier B.V. All rights reserved.