Models for the Impact of All Order Book Events
The relation between order flow and price changes has attracted considerable attention in recent years (see Hasbrouck, 2007; Mike and Farmer, 2008; Bouchaud et al., 2004, 2006, 2009; Lyons, 2006). Most empirical studies to date have focused on the impact of (buy/sell) market orders. Many interesting results have been obtained, such as the very weak dependence of impact on the volume of the market order, the long-range nature of the sign of the trades, and the resulting nonpermanent, power-law decay of market order impact with time (see Bouchaud et al., 2009). However, this representation of impact is incomplete in at least two ways. First, the impact of all market orders is usually treated on the same footing, or with a weak dependence on volume, whereas some market orders are “aggressive” and immediately change the price, while others are more passive and only have a delayed impact on the price. Second, other types of order book events (limit orders, cancellations) must also directly impact prices: adding a buy limit order induces extra upwards pressure and cancelling a buy limit order decreases this pressure. Within a description based on market orders only, the impact of limit orders and cancellations is included in an indirect way, in fact as an effectively decaying impact of market orders. This decay reflects the “liquidity refill” mechanism explained ...