The scaling properties of oil price fluctuations are described as a non-stationary stochastic process realized by a time series of finite length. An original model is used to extract the scaling exponent of the fluctuation functions within a non-stationary process formulation. It is shown that, when returns are measured over intervals less than 10 days, the Probability Density Functions (PDFs) exhibit self-similarity and monoscaling, in contrast to the multifractal behavior of the PDFs at macro-scales (typically larger than one month). We find that the time evolution of the distributions are well fitted by a Levy distribution law at micro-scales. The relevance of a Levy distribution is made plausible by a simple model of nonlinear transfer
