Analyzing an Electronic Limit Order Book

by David Kane, Andrew Liu, and Khanh Nguyen

Abstract The orderbook package provides fa- cilities for exploring and visualizing the data associated with an order book: the electronic collection of the outstanding limit orders for a financial instrument. This article provides an overview of the orderbook package and exam- ples of its use.

Introduction

The orderbook package provides facilities for ex- ploring and visualizing the data associated with an order book: the electronic collection of the outstand- ing limit orders for a financial instrument, e.g. a stock. A limit order is an order to buy or sell a given quantity of stock at a specified limit price or better. The size is the number of shares to be bought or sold. An order remains in the order book until fully exe- cuted, i.e. until its size is zero as a result of trades. Partial executions occur as a result of trades for less than the entire size of the order.
Consider a simple order book containing five limit orders: sell 150 shares of IBM at $11.11, sell 150 shares of IBM at $11.08, buy 100 shares of IBM at $11.05, buy 200 shares of IBM at $11.05, and buy 200 shares of IBM at $11.01.

cancel/replace orders can identify the correspond- ing limit order. A market order is an order to im- mediately buy or sell a quantity of stock at the best available prices. A trade occurs when a market or- der “hits” a limit order on the other side of the inside market.
All orders have timestamps indicating the time at which they were accepted into the order book. The timestamp determines the time priority of an order. Earlier orders are executed before later orders. For example, suppose that the order to buy 100 shares at $11.05 was submitted before the order to buy 200 shares at $11.05. Now suppose a market order sell- ing 200 shares is submitted to the order book. The limit order for 100 shares will be executed because it is at the front of the queue at the best bid. Then, 100 shares of the order with 200 total shares will be exe- cuted, since it was second in the queue. 100 shares of the 200 share order remain in the order book at
$11.05.
| Price | Ask Size | | $11.11 | 50 | 100 | $11.05 | | 200 | $11.01 | | Bid Size | Price | |

A market order for more shares than the size at the inside market will execute at worse price levels until it is complete. For example, if a market order to buy 200 shares is submitted to the order book, the or- der at $11.08 will be fully executed. Since there are no more shares available at that price level, 100 shares at the $11.11 price level will be transacted to complete the market order. An order to sell 50 shares at $11.11 will remain in the order book. Executing these two market orders (a sell of 200 shares and a buy of 200 shares) on our hypothetical order book results in a new state for the order book.

| Price$11.11 | Ask150 | Size | | $11.08 | 100 | | 300 | $11.05 | | | 200 | $11.01 | | | Bid Size | Price | | |

Orders on the bid (ask ) side represent orders to buy (sell). The price levels are $11.11, $11.08, $11.05, and
$11.01. The best bid at $11.05 (highest bid price) and the best ask at $11.08 (lowest ask price) make up the inside market . The spread ($0.03) is the difference between the best bid and best ask. The midpoint ($11.065) is the average of the best bid and best ask.
There are four types of messages that traders can submit to an order book: add , cancel , can- cel/replace, and market order. A trader can add a limit order in to the order book. She can also can- cel an order and remove it from the order book. If a trader wants to reduce the size of her order, she can issue a cancel/replace, which cancels the order, then immediately replaces it with another order at the same price, but with a lower size. Every limit order is assigned a unique ID so that cancel and

Note that cancel/replace orders can lower the size of an order, but not increase it. Cancel/replace orders maintain the time priority of the original or- der, so if size increases were allowed, traders with orders at the highest time priority for a price level could perpetually increase the size of their order, pre- venting others from being able to transact stock us- ing limit orders at that price level. See Johnson (2010) for more details on the order book.

Example

NVIDIA is a graphics processing unit and chipset de- veloper with ticker symbol NVDA. Consider the or- der book for NVDA at a leading electronic exchange

on June 8, 2010. We create the orderbook object by specifying the location of our data file.

> library(orderbook)
> filename <- system.file("extdata", + "sample.txt", + package = "orderbook")
> ob <- orderbook(file = filename)
> ob <- read.orders(ob, 10000)

> ob

An object of class orderbook (default) Current orderbook time: | 09:35:02 | Message Index: | 10,000 | Bid Orders: | 631 | Ask Orders: | 1,856 | Total Orders: | 2,487 |

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> display(ob)

Current time is 09:35:02

Price Ask Size
---------------------------------------------
11.42 900 11.41 1,400 11.40 1,205 11.39 1,600 11.38 400 2,700 | 11.36 | 1,100 | 11.35 | 1,100 | 11.34 | 1,600 | 11.33 | 700 | 11.32 |

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We read in the first 10,000 messages then show the object. The current time is 9:35:02 AM. This is the time of the last message read. The message index in- dicates which row in the data file the object has read through. The display also shows that there are 631 bids and 1,856 asks outstanding, for a total of 2,487 orders. This indicates that many earlier orders have

--------------------------------------------- Bid Size Price

display shows the inside market, along with the four next best bid and ask price levels and the size at each price level.

> plot(ob)

Order Book − 09:35:02

been removed through either cancels or trades.

> summary(ob)

BID

ASK

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12.60

12.40

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12.20

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Current time is 09:35:02 ● ● ●
● 12.00
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Ask price levels: 540

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11.80

Bid price levels: 179
Total price levels: 719
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Price
11.36

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11.60

11.38

Ask orders: 1,856

11.20 ● ● ● ●
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Bid orders: 631 Total orders: 2,487
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Spread: 0.02 Mid point: 11.37
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Best Bid: | 11.36 | Size: | 2,700 | Best Ask: | 11.38 | Size: | 400 |

Inside market

11.00

10.80

10.60

10.40

10.20

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Size (Shares)

Using summary the total order information from show is repeated. Additionally, we see that there are 540 ask and 179 bid price levels, for a total of 719. This indicates that many orders have been submitted at the same price level. The spread is $0.02, and the midpoint is $11.37. The inside market is composed of 2,700 shares offered at the best bid of $11.36 and 400 shares offered at the best ask of $11.38.

plot is a graphical representation of display. Price levels are on the y-axis, and size is on the x-axis. The maximum and minimum price levels displayed by default are 10% above and below the midpoint. Note the large number of shares at $11.01. It is help- ful to know the number of orders which make up the large size at that price level. Using the "[" method we can view the order information at particular price levels.