2 Linear and permanent impact : The Kyle model

1 What is price impact? Price impact refers to the correlation between an incoming order (to buy or to sell) and the subsequent price change. That a buy trade should push the price up seems at first sight obvious and is easily demonstrated empirically, as we will review below. It is also a dour reality for traders for whom price impact is tantamount to a cost: their second buy trade is on average more expensive than the first because of their own impact (and vice-versa for sells). Monitoring and controling impact is therefore one of the most active and rapidly expanding domains of research within trading firms. The most important questions are related to the volume dependence of impact (do larger trades impact prices more?), and the temporal behaviour of impact (is the impact of a trade immediate and permanent, or is there some lag dependence of the impact?). A moment of reflection suggests that the interpretation of price impact is far from trivial, and may even lead to contradictions – isn't a transaction a fair deal between a buyer and a seller? So why is there price impact? Three distinct possibilities come to mind: 1. Agents successfully forecast short term price movements and trade accordingly. This can result in measurable correlation between trades and price changes, even if the trades by themselves have absolutely no effect on prices at all. If an agent correctly forecasts price movements and if the price is about to rise, the agent is likely to buy in anticipation of it. But in this framework 'noise induced' trades, based on no information at all, should have no price impact.