Introduction

Elaborating on the results presented in Section 2.6, this chapter focuses on the shape of limit order books and the influence of the size of incoming orders. It confirms the theoretical findings of the models studied in Chapters 6 and 7.

Methodology

We use the order book data described in Appendix B.3. All movements on the first 10 limits of the ask side and the bid side of the order book are available, which allows us to reconstruct the evolution of the first limits of the order book during the day. Each trading day is divided into 12 thirty-minute intervals from 10am to 4pm. We obtain T = 391 intervals for each stock (three and a half days of trading are missing or incomplete in our dataset: January 15th, the morning of January 21st, February 18th and 19th). For each interval t = 1,..., T, and for each stock k = 1,..., 14, we compute the total number of limit orders Lk(t) and market orders Mk(t), and the average volume (in euros) of limit orders VkL (t) and market orders Vkm(t). Table 3.1 gives the average number of orders and their volumes (the overline denotes the average over the time intervals:, and similarly for other quantities). The lowest average activity is observed on UBIP.PA and LAGA.PA (which are the only two stocks in the sample with less than 200 market orders and 4000 limit orders in average). The highest activity is observed on BNPP.PA (which is the only stock with more than 600 market orders and 6000 limit orders on average). The smallest sizes of orders are observed on AIRP.PA (108.25 and 205.4 for market and limit orders), and the largest sizes are observed on AXA.PA (535.6 and 876.6 for market and limit orders).

We also compute the average cumulative order book shape at 1 to 10 ticks from the best opposite side. Denoting by PB(t) and PA(t) the best bid and ask prices at time t, the average cumulative depth Bki (t) is the cumulative quantity available in the order book for stock k in the price range {PB(t) + 1,..., PB(t) + i} (in ticks) for ask limit orders, or in the price range {PA(t)- i,..., PA(t)- 1} for bid limit orders, averaged over time during interval t.