Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''

TL;DR

This paper uncovers a causal information cascade in stock market volatility across different time scales, revealing a flow from large to small scales using wavelet analysis, which enhances understanding of market dynamics.

Contribution

It introduces a wavelet-based method to identify and quantify a causal information cascade in stock market volatility across scales, providing new insights into market dynamics.

Findings

Evidence of a causal information cascade from large to small scales.

Visualization of information flux across different time scales.

Interpretation of findings in terms of market dynamics.

Abstract

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.