  Modelling accurately financial price variations is an essential step
underlying portfolio allocation optimization, derivative pricing and hedging,
fund management and trading. The observed complex price fluctuations guide and
constraint our theoretical understanding of agent interactions and of the
organization of the market. The gaussian paradigm of independent normally
distributed price increments has long been known to be incorrect with many
attempts to improve it. Econometric nonlinear autoregressive models with
conditional heteroskedasticity (ARCH) and their generalizations capture only
imperfectly the volatility correlations and the fat tails of the probability
distribution function (pdf) of price variations. Moreover, as far as changes in
time scales are concerned, the so-called ``aggregation'' properties of these
models are not easy to control. More recently, the leptokurticity of the full
pdf was described by a truncated ``additive'' L\'evy flight model (TLF).
Alternatively, Ghashghaie et al. proposed an analogy between price dynamics and
hydrodynamic turbulence. In this letter, we use wavelets to decompose the
volatility of intraday (S&P500) return data across scales. We show that when
investigating two-points correlation functions of the volatility logarithms
across different time scales, one reveals the existence of a causal information
cascade from large scales (i.e. small frequencies, hence to vocable
``infrared'') to fine scales (``ultraviolet''). We quantify and visualize the
information flux across scales. We provide a possible interpretation of our
findings in terms of market dynamics.
