Notes for /Trades, Quotes, and Prices/

git clone git://
commit c60e20082fd1b5be88466e4d6f15839ac336281c
parent d6e413a49fca0789606f404e274a2ac654930a39
Author: Shimmy Xu <>
Date:   Thu,  7 May 2020 14:41:13 -0500

Add notes for Chapter 04

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@@ -188,7 +188,32 @@ Most common priority rules include price-time and pro-rata. Priority rules do af
 The actions of traders in an LOB can be expressed solely in terms of the submission or cancellation of orders of lot size \(\v_{0}\). Common order types include stop orders, iceberg orders, IOC/FOK orders, and market-on-close (MOC) orders. A MOC order is a market order that is submitted to execute as close to the closing price as possible, mostly to take advantage of the larger liquidity at close.
 For exchanges that are closed overnight, beginning and end of trading day may see so much volume that LOB trading would be prone to instabilities, so exchanges prefer to use auctions at those times. Auction clearing price is visible throughout, and traders can use this information to adjust their orders.
-  p_{t}
-  &= p_{0} + \mean{p}(\sum_{t' = 0}^{t - 1}r_{t'} + \eta_{t}).
+* Chapter 04
+Large tick vs. small tick: if tick size is comparable to spread, then it's large tick; if tick size is way smaller than spread, then it's small tick.
+This chapter is basically stylized facts for order books.
+- Summary Statistics
+  1. Daily turnover around 0.5% of market cap. This has doubled from 1995 to 2015.
+  2. Total volume in LOB within 1% of mid price (around half day's vol range), is 1-3% of daily traded volume, a rather small percentage.
+  3. Top level activity are more abundant in large tick stocks and is on a sub-second time scale. This reflect importance of queue position for large tick stocks.
+  4. Number of trade-throughs is a few percent for small tick name, and a few per thousand for large-tick stocks.
+- Intra-day Patterns. These apply to between 10:30-15:00 local time when most quantities have a flat average profile, away from open/close auctions.
+  1. Market activity exhibits a U-shape profile, much more violent at beginning and end of day. This could be caused by overnight news, trader rushing at last minute, or their execution patterns.
+  2. Average spread narrows through out the day, and small tick stocks show larger scale changes. This suggests liquidity at open is a lot more expansive, possibly due to stronger adverse selection caused by overnight news.
+- Tail of spread distribution is roughly exponential. Large/small tick stocks differ in the peak of distribution, and spread is generally narrower right before transactions.
+- Arrival rate distribution looks different for large/small tick stocks, but both with tail decay slower than power law. Large ticks' distribution decays monotonously with most orders at best quote, while that for small ticks has a secondary peak at 2x spread, with many levels in between empty, meaning that spread, instead of tick sizes is determining the distribution. Cancellation rates is to first order, proportional to arrival rate.
+- Order size distribution's upper tail roughly follows power law with exponent \(-\frac{5}{2}\). Generally order sizes are not clustered, but distributed over a broad range.
+- Volume at best quotes has similar distribution to order sizes. For small tick stocks, when trades happen, volume at best quote is higher (more liquidity); for large tick stocks, when trades happen, volume in queue is lower (meaning price may move soon).
+- Volume (book depth) profile is similar to arrival rate: increases sharply to typical spread before decaying very slowly beyond that. Volume can peak at round prices as they are favored over others. Empty levels is also a lot more common in small tick stocks.
+- Tick size effects.
+  1. When relative tick \(\vartheta_{r}\) is small, spread is roughly proportional to price (around one thousandth of price).
+  2. Volume at best quote is higher for large tick stocks. Note that small tick stock are also likely high-priced, the same sized lot is a lot more expansive.
+  3. Orders in small tick stocks consume more of the outstanding volume percentage wise (>50%), but the available volume is also frequently lower.
+Relative tick size is what seems to differentiate different stock's behaviors the most.
+Most market metrics are symmetric between buys and sells when averaged over a suitably long horizon.
+All the size distributions (limit/market orders and best quote volumes) have heavy tails.