More statistical properties of order books and price impact Marc Potters

We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time of a limit order as a function of the distance from the best price. We also determine the ‘price impact’ function using French and British stocks, and find a logarithmic, rather than a power-law, dependence of the price response on the volume. The weak time dependence of the response function shows that the impact is, surprisingly, quasi-permanent, and suggests that trading itself is interpreted by the market as new information. Many statistical properties of financial markets have already been explored, and have revealed striking similarities between very different markets (different traded assets, different geographical zones, different epochs) [1, 2, 3]. More recently, the statistics of the ‘order book’, which is the ultimate ‘microscopic’ level of description of financial markets, has attracted considerable attention, both from an empirical [4, 5, 6, 8, 7] and theoretical [9, 10, 5, 11, 12, 13, 8, 14, 15] point of view. The order book is the list of all buy and sell limit orders, with their corresponding price and volume, at a given instant of time. We will call a(t) the ask price (best sell price) at time t and b(t) the bid price (best buy price) at time t. The midpoint m(t) is the average between the bid and the ask: m(t) = [a(t)+ b(t)]/2.