COMP226 Assignment 1: Reconstruct a Limit Order Book
Continuous Assessment Number
1 (of 2)
Assignment Circulated
09:00 Tuesday 18 February 2020 (updated 2020-02-20)
17:00 Friday 6 March 2020
Submission Mode
Electronic only
Submit a single file “MWS-username.R”, where MWS-username should be replaced with your MWS username.
Learning Outcomes Assessed
Have an understanding of market microstructure and its impact on trading.
Goal of Assignment
Reconstruct a limit order book from order messages
Marking Criteria
Code correctness (85%); Code readability (15%)
Submission necessary in order to satisfy module requirements
Late Submission Penalty
Standard UoL policy; resubmissions after the deadline will NOT be considered.
Expected time taken
Roughly 8-12 hours
Your code will be put through the department’s automatic plagiarism and collusion detection system. Student’s found to have plagiarized or colluded will likely receive a mark of zero. Do not discuss or show your work to others. In previous years, two students had their studies terminated and left without a degree because of plagiarism.
Rscript from Rstudio
In this assigment, we use Rscript (which is provided by R) to run our code, e.g., Rscript skeleton.R input/book_1.csv input/empty.txt
In R studio, you can call Rscript from the “terminal” tab (as opposed to the “console”). On Windows, use Rscript.exe not Rscript:
Rscript.exe skeleton.R input/book_1.csv input/empty.txt

Distributed code and sample input and output data
As a first step, please download comp226_a1.zip comp226_a1_v3.zip from: https://student.csc.liv.ac.uk/internal/modules/comp226/_downloads/comp226_a1_v3.zip
Then unzip comp226_a1.zip, which will yield the following contents in the directory comp226_a1:
├── input
│ ├── book_1.csv
│ ├── book_2.csv
│ ├── book_3.csv
│ ├── empty.txt
│ ├── message_a.txt
│ ├── message_ar.txt
│ ├── message_arc.txt
│ ├── message_ex_add.txt
│ ├── message_ex_cross.txt
│ ├── message_ex_reduce.txt
│ └── message_ex_same_price.txt
├── output
│ ├── book_1-message_a.out
│ ├── book_1-message_ar.out
│ ├── book_1-message_arc.out
│ ├── book_2-message_a.out
│ ├── book_2-message_ar.out
│ ├── book_2-message_arc.out
│ ├── book_3-message_a.out
│ ├── book_3-message_ar.out
│ └── book_3-message_arc.out
└── skeleton.R
2 directories, 21 files
Brief summary
The starting point for the assignment is a code skeleton, provided in a file called skeleton.R. This file runs without error, but does not produce the desired output because it contains 6 empty functions. To complete the assignment you will need to correctly complete these 6 functions.
You should submit a single R file that contains your implementation of some or ideally all of these 6 functions. Your submission will be marked via a combination of:
• automated tests (for code correctness, 85%, breakdown by function given below); and
• human visual inspection (for code readability, 15%, in particular, for appropriate naming of variables and functions (5%), good use of comments (5%), and sensible, consistent code formatting (5%)).
Correct sample output is provided so that you can check whether your code implemetations produces the correct output.

skeleton.R versus solution.R
You are given skeleton.R, which you should extend by implementing 6 functions. Throughout this handout, we also generate example output using a file solution.R that contains a correct implementation of all 6 of these functions. Obviously, you are not given the file solution.R, however the example output will be helpful for checking that your function implementations work correctly.
Two sets of functions to implement
As described in detail in the rest of this document, you are required to implement the following 6 functions. The percentage in square brackets correspond to the breakdown of the correctness marks by function.
Limit order book stats:
1. book.total_volume <- function(book) [10%] 2. book.best_prices <- function(book) [10%] 3. book.midprice <- function(book) [10%] 4. book.spread <- function(book) [10%] Updating the limit order book: 5. book.reduce <- function(book, message) [15%] 6. book.add <- function(book, message) [30%] Running skeleton.R An example of calling skeleton.R follows. Rscript skeleton.R input/book_1.csv input/empty.txt As seen in this example, skeleton.R takes as arguments the path to two input files: 1. initial order book (input/book_1.csv in the example) 2. order messages to be processed (input/empty.txt in the example) Note: the order of the arguments matters. Let’s see part of the source code and the output that it produces. Warning Do not make changes to the rest of the code in skeleton.R, only implement these 6 functions. Penalties may be applied if other changes are present in your submission. if (! { interactive()) options (warn= ) -1 args <- commandArgs(trailingOnly = TRUE) if( ( ) 2){ ( “)
book_path <- args[1]; data_path <- args[2] if (! (data_path) ! (book_path)) { () book <- book.load(book_path) book <- book.reconstruct(data.load(data_path), init=book) book.summarise(book) } length args != stop “Must provide two arguments: file.exists || file.exists stop “File does not exist at path provided.” } So in short, this part of the code: • checks that there are two command line arguments • assigns them to the appropriate variables (the first to the initial book file path, the second to the message file path) • loads the initial book • reconstructs the book according to the messages • prints out the book • prints out the book stats Let’s see the output for the example above: $ Rscript skeleton.R input/book_1.csv input/empty.txt $ask oid price size 1 a 105 100 $bid oid price size 1 b 95 100 Total volume: Best prices: Mid-price: Spread: Now let’s see what the output would look like for a correct implementation: $ Rscript solution.R input/book_1.csv input/empty.txt $ask oid price size 1 a 105 100 $bid oid price size 1 b 95 100 Total volume: Best prices: Mid-price: Spread: 10 100 100 95 105 100 You will see that now the order book stats have been included in the output, because the four related functions that are empty in skeleton.R have been implemented in solution.R. The initial order book Here is the contents of input/book_1.csv, which is one of the 3 provided examples of an initial book: Let’s justify the columns to help parse this input: The first row is a header row. Every subsequent row contains a limit order, which is described by the following fields: • oid (order id) is stored in the book and used to process (partial) cancellations of orders that arise in “reduce” messages, described below; • side identifies whether this is a bid (‘B’ for buy) or an ask (‘S’ for sell); • price and size are self-explanatory. Existing code in skeleton.R will read in a file like input/book_1.csv and create the corresponding two (possibly empty) orders book as two data frames that will be stored in the list book, a version of which will be passed to all of the six functions that you are required to implement. Note that if we now change the message file to a non-empty one, skeleton.R will produce the same output (since it doesn’t parse the messages; you need to write the code, functions 5 and 6, to do that): oid,side,price,size a,S, , b,B, , 105 100 95 100 oid side price size a S 105 100 b B 95 100 $ Rscript skeleton.R input/book_1.csv input/message_a.txt $ask oid price size 1 a 105 100 $bid oid price size 1 b 95 100 Total volume: Best prices: Mid-price: Spread: If correct message parsing and book updating is implemented, book would be updated according to input/adds_only.txt to give the following output: $ Rscript solution.R input/book_1.csv input/message_a.txt $ask oid price size 8a 7o 6r 5k 4q 3m 2j 1n $bid oid price size 1b 2l 3p 4s Total volume: Best prices: Mid-price: .5 Spread: 1 105 104 102 100 292 194 99 98 98 97 96 71 166 88 132 375 95 95 94 91 100 29 87 102 318 1418 95 96 95 Before we go into details on the message format and reconstructing the order book, let’s discuss the first four functions that compute the book stats, which we also see correctly computed in this example. Computing limit order book stats The first four of the functions that you need to implement compute limit order book stats, and can be developed and tested without parsing the order messages at all. In particular, you can develop and test the first four functions using an empty message file, input/empty.txt, as in the first example above. The return values of the four functions should be as follows (where as usual in R single numbers are actually numeric vectors of length 1): • book.total_volumes should return a list with two named elements, bid, which should contain the total volume in the bid book, and ask, which should contain the total volume in the ask book; • book.best_prices <- function(book) should return a list with two named elements, bid, which should contain the best bid price, and ask, which should contain the best ask price; • book.midprice should the midprice of the book; • book.spread should the spread of the book; You should check that the output of these functions in the example above that uses solution.R are what you expect them to be. We now move on to the reconstructing the order book from the messages in the input message file. Reconstructing the order book from messages You do not need to look into the details of the (fully implemented) functions book.reconstruct or book.handle that manage the reconstruction the book from the starting initial book according to the messages. In the next section, we describe that there are two types of message, “Add” messages and “Reduce” messages. All you need to know to complete the assignment is that messages in the input file are processed in order, i.e., line by line, with “Add” messages passed to book.add and “Reduce” messages passed to book.reduce, along with the current book in both cases. Message Format The market data log contains one message per line (terminated by a single linefeed character, ‘\n’), and each message is a series of fields separated by spaces. There are two types of messages: “Add” and “Reduce” messages. Here’s an example, which contains an “Add” message followed by a “Reduce” message: An “Add” message looks like this: ‘A’ oid side price size • ‘A’: fixed string identifying this as an “Add” message; • oid: “order id” used by subsequent “Reduce” messages; • side: ‘B’ for a buy order (a bid), and an ‘S’ for a sell order (an ask); • price: limit price of this order; • size: size of this order. A “Reduce” message looks like this: ‘R’ oid size • ‘R’: fixed string identifying this as a “Reduce” message; • oid: “order id” identifies the order to be reduced; • size: amount by which to reduce the size of the order (not the new size of the order); if size is equal to or greater than the existing size of the order, the order is removed from the book. Processing messages “Reduce” messages will affect at most one existing limit order in the book. “Add” messages will either: • not cross the spread and then add a single row to the book (orders at the same price are stored separately to preserve their distinct “oid”s); • cross the spread and in that case can affect any number of orders on the other side of the book (and may or may not result in a remaining limit order for residual volume). A c S 97 36 R a 50 The provided example message files are split into cases that include crosses and those that don’t to help you develop your code incrementally and test it on inputs of differing difficulty. We do an example of each case, one by one. In each example we start from input/book_1.csv; we only show this initial book in the first case. Example of processing a reduce message $ Rscript solution.R input/book_1.csv input/empty.txt $ask oid price size 1 a 105 100 $bid oid price size 1 b 95 100 Total volume: 100 100 Best prices: 95 105 Mid-price: 100 Spread: 10 $ cat input/message_ex_reduce.txt R a 50 $ Rscript solution.R input/book_1.csv input/message_ex_reduce.txt $ask oid price size 1 a 105 50 $bid oid price size 1 b 95 100 Total volume: 100 50 Best prices: 95 105 Mid-price: 100 Spread: 10 Example of processing an add (non-crossing) message $ cat input/message_ex_add.txt A c S 97 36 $ Rscript solution.R input/book_1.csv input/message_ex_add.txt $ask oid price size 2 a 105 100 1 c 97 36 $bid oid price size 1 b 95 100 Total volume: 100 136 Best prices: 95 97 Mid-price: 96 Spread: 2 Example of processing a crossing add message $ cat input/message_ex_cross.txt A c B 106 101 $ Rscript solution.R input/book_1.csv input/message_ex_cross.txt $ask [1] oid price size <0 rows> (or 0-length row.names)
oid price size
1 c 106 1
2 b 95 100
Total volume: 101 0
Best prices: 106 NA
Mid-price: NA
Spread: NA
Sample output
We provide sample output for 9 cases, namely all combinations of the following 3 initial books and 3 message files.
The 3 initial books are found in the input subdirectory and are called:
• book_1.csv • book_2.csv • book_3.csv

The 3 message files are also found in the input subdirectory and are called:
add messages only, i.e., requires book.add but not book.reduce; for all three initial books, none of the messages cross the spreed
add and reduce messages, but for the initial book book_3.csv, no add message crosses the spread
add and reduce messages, with some adds that cross the spread for all three initial books
The 9 output files can be found in the output subdirectory of the comp226_a1 directory.
├── book_1-message_a.out
├── book_1-message_ar.out
├── book_1-message_arc.out
├── book_2-message_a.out
├── book_2-message_ar.out
├── book_2-message_arc.out
├── book_3-message_a.out
├── book_3-message_ar.out
└── book_3-message_arc.out
0 directories, 9 files
Hints for order book stats
For book.spread and book.midprice a nice implementation would use book.best_prices, which you should then implement first.
Hints for book.add and book.reduce
A possible way to implement book.add and book.reduce that makes use of the different
example message files is the following:
• First, do a partial implementation of book.add, namely implement add messages that do not cross. Check your implementation with message_a.txt.
• Next, implement book.reduce fully. Check your combined (partial) implementation of book.add and book.reduce with message_ar.txt and book_3.csv (only this combination with message_ar.txt has no crosses).
• Finally, complete the implementation of book.add to deal with crosses. Check your implementation with message_arc.txt and any initial book or with message_ar.txt and book_1.csv or book_2.csv.
Hint on book.sort
In comp226_a1_v3 there is a book.sort method, with sort code as follows:
book.sort <- (book, sort_bid=T, sort_ask=T) { if (sort_ask && (book$ask) >= 1) {
book$ask <- book$ask[order(book$ask$price, nchar(book$ask$oid), book$ask$oid, function nrow decreasing=F),] row.names(book$ask) <- 1:nrow(book$ask) } if (sort_bid && nrow(book$bid) >= 1) {
book$bid <- book$bid[order(-book$bid$price, nchar(book$bid$oid), book$bid$oid, decreasing=F),] row.names(book$bid) <- 1:nrow(book$bid) } book } This method will ensure that limit orders are sorted first by price and second by time of arrival (so that for two orders at the same price, the older one is nearer the top of the book). You are welcome (and encouraged) to use book.sort in your own implementations. In particualar, by using it you can avoid having to find exactly where to place an order in the book. Hint on using logging in book.reconstruct In comp226_a1_v3 a logging option has been added to book.reconstruct: book.reconstruct <- function(data, init=NULL, log=F) { ( ( book <- }, 1:nrow(data), init, ) book.sort(book) } if if nrow (data) 0) return(book) (init init <- book.init() ( (b, i) { new_book <- book.handle(b, data[i,]) if( ){ (“Step”, i, “\n\n”) book.summarise(new_book, with_stats=F) cat(“====================\n\n”) } new_book == is.null )) Reduce function log cat You can turn on logging by changing log=F to log=T. Then book.summarise will be used to give output after each message is processed by book.reconstruct. Hint on stringsAsFactors=FALSE Notice the use of` stringsAsFactors=FALSE in the book.load function (similarly in data.load) from skeleton.R. book.load <- function(path) { df <- read.table( path, fill=NA, stringsAsFactors=FALSE, header=TRUE, sep=’,’ ) book.sort(list( =df[df , c( , , , =df[df , c( , , )) } “size”)] “size”)] ask bid $side $side == == “S” “B” “oid” “oid” “price” “price” Its use here is not optional, it is necessary and what ensures that the oid column of book$bid and book$ask have type character. It is also crucial that you make sure that you ensure that the type of your oid columns in your books remain character rather than factors. The following examples will explain the use of stringsAsFactors and help you to achieve this. First we introduce a function that will check the type of this column on different data frames that we will construct: check <- (df) { checks <- c( , check, eval(parse(text=check))), ‘\n’) function “is.character(df$oid )” “is.factor(df$oid)” ) for (check in checks) cat(sprintf(“%20s: %5s”, } Now let’s use this function to explore different cases. First we look at the case of reading a csv. What about creating a data.frame? What about using rbind? > check(read.csv(
is.character(df ): FALSE
is.factor(df ): TRUE
> check(read.csv(
is.character(df ): TRUE
is.factor(df ): FALSE
, stringsAsFactors=FALSE))
$oid $oid
$oid $oid
> check(data.frame(oid=”a”, price=1))
is.character(df ): FALSE
is.factor(df ): TRUE
> check(data.frame(oid=”a”, price=1, stringsAsFactors=FALSE))
is.character(df ): TRUE
is.factor(df ): FALSE
$oid $oid
$oid $oid

> empty_df <- data.frame(oid=character(0), =numeric(0 > non_empty_df <- data.frame(oid=”a”, =1, =FALSE) > check(rbind(empty_df, data.frame(oid=”a”, price=1)))
is.character(df ): FALSE
is.factor(df ): TRUE
> check(rbind(empty_df, non_empty_df))
is.character(df ): TRUE
is.factor(df ): FALSE
> check(rbind(non_empty_df, data.frame(oid=”a”, price=1)))
is.character(df ): TRUE
is.factor(df ): FALSE
$oid $oid
$oid $oid
$oid $oid
Note that with a non-empty data frame, the existing type persists! However, when the data.frame is empty the type of the oid column is malleable and it is crucial to use stringsAsFactors=FALSE. We see the same behaviour when we rbind a list with a data.frame.
> check(rbind(empty_df, list(oid=”a”, price=1)))
is.character(df ): FALSE
is.factor(df ): TRUE
> check(rbind(empty_df, list(oid=”a”, price=1), stringsAsFactors=FALSE))
is.character(df ): TRUE
is.factor(df ): FALSE
> check(rbind(non_empty_df, list(oid=”a”, price=1)))
is.character(df ): TRUE
is.factor(df ): FALSE
$oid $oid
$oid $oid
$oid $oid
Again, it is crucial to use stringsAsFactors=FALSE when the data.frame is empty. I suggest to use it in every case.
Remember to submit a single “MWS-username.R” file, where MWS-username should be replaced with your MWS username.

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