Abstract: The impact of large trades on market prices is a widely discussed but rarely measured phenomenon, of essential importance to selland buy-side participants. We analyse a large data set from the Citigroup US equity trading desks, using a simple but realistic theoretical framework. We fit the model across a wide range of stocks, determining the dependence of the coefficients on parameters such as volatility, average daily volume, and turnover. We reject the common square-root model for temporary impact as function of trade rate, in favor of a 3/5 power law across the range of order sizes considered. Our results can be directly incorporated into optimal trade scheduling algorithms and pre- and post-trade cost estimation.

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: strongly correlated market or- ders 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 mar- ket 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 discuss the information content of each trade, and find that it is on average very small.