Modeling the co-movements between crude oil and refined petroleum markets

In this paper we investigate two types of asymmetries, i.e., the asymmetry in the lower and upper tail dependences and the asymmetry in the propagation of crisis (bubble), between crude oil market and refined petroleum markets based on copula models. Thirteen copula models with different types of dependence structures and time-varying dependence parameters are considered. We find that in general the MALM copula fits our sample data best based on AIC criterion. We find that lower and upper tail dependences are both positive indicating that crude oil and refined product markets tend to move together. Using the asymmetric copulas, we find asymmetry in tail dependence between crude oil and heating oil returns and that between crude oil and jet fuel returns. Interestingly, upper tail dependence is significantly greater than the lower tail dependence for the pre-crisis period, while the result is reversed for the post-crisis period. Finally, although our data prefers the nonexchangeable MALM copula, the asymmetry in the propagation of crisis (bubble) between crude oil and refined product returns is very weak.