Abstract: The quantile of oil futures return can reveal the character of distribution and measure extreme riskso, so it is necessary to model the quantile of oil futures return and analyze the dynamics of quantile. Considering the shortage of current research and the asymmetric influences of positive and negative oil return on quantile, threshold CAViaR model is developed and adopted to analyze the quantile of oil futures return. Using daily data of Brent crude oil futures price spanning from 1998 to 2009, the results show the quantile of oil futures return has autoregressive effect and is affected by lagged oil return. Besides, the positive return has stronger influence on quantile than the negative return. Oil price movement will affect the quantile of left tail, but only the decrease of oil price will make the quantile of right tail change. Moreover, the quantile is related to VaR, so the results can reveal the character of oil price risk and have important implications in risk management.

Key words: oil futures, quantile regression, QAR model, CAViaR model, threshold CAViaR model