Fluctuations and response in financial markets: the subtle nature of `random' price changes

TL;DR

This paper investigates the delicate balance between persistent and mean-reverting forces in financial markets, revealing how their interplay results in the seemingly random yet complex nature of price changes.

Contribution

It introduces a model capturing the market's response to trades via a non-constant propagator, demonstrating the market operates at a critical point with diffusive prices.

Findings

Prices are at a critical point with diffusive behavior.

Empirical and theoretical evidence of a fluctuation-response relation.

The fraction of truly informed orders is small.

Abstract

Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to super-diffusion (or persistence), and mean reverting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non constant `propagator' in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We find empirically, and discuss theoretically, a fluctuation-response relation. We also discuss the fraction of truly informed market orders, that correctly anticipate short term moves, and find that it is quite small.