## Motivation

The motivation behind gaining a better understanding of volume is not merely theoretical, but it equally has a great practical relevance. On order-driven markets, if a submitted buy (sell) market order is relatively large compared to the market, it will possibly swipe out several price levels; thus, the achieved average price on the entire trade will be higher (lower) than the best price level at the moment of order submission, and the submitter loses money. This phenomenon is often referred to as price impact, and it is well worth making an effort to avoid or at least minimize it.

One way to do this is to perform order splitting, that is, splitting a market order into smaller chunks and submitting them gradually. Among the numerous logics behind splitting, a popular one is the **volume weighted average price** (**VWAP**) strategy that aims to obtain the daily weighted average price where weights are determined by the volume transacted relative to the total daily volume. Long-term investors...