  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
