Liquidity and Self-Similarity in the Distributions of the log price variations

Self-similarity is implicit in the standard modeling of financial markets, when a Brownian motion or an a-stable process are assumed for the dynamics of prices. Irrespective of the self-similarity parameter, one rationale for the price process to be self-similar is based on the idea that the different investment horizons to whom the operators look at when they take their trading decisions, cancel the diversities in the perception of the risk, once the price variations are properly standardized. Thus, the short position of an intraday trader experiencing a large-sigma event related to the timeframe of his dataset can match the long position of the long-term trader, who can judge negligible the variation, given his timeframe. In this interpretation of the market mechanism, high liquidity should be observed when such condition of scale invariance holds. Vice versa, when some catastrophic event occurs, the scale invariance is usually disrupted, since the increasing uncertainty induces investors to move abruptly towards shorter horizons or not to increase their exposure. This can increase the level of illiquidity in financial markets. Equipped with this financial interpretation, the paper analyzes how the extent of self-similarity changes through time and relates this behavior to the level of liquidity which characterizes the main financial markets.