Kraken technical assessment: matching engine

How to

Build

This project was written on a Linux (NixOS) machine, using the CMake build system.

To build the project you should run the following commands:

mkdir build
cmake -B build
cmake --build build

To run unit and integration tests you can use:

cmake --build build --target test

Run

The kraken binary should be built in build/src/kraken. You can see example inputs and their matching outputs in the data/ directory at the root of the repository.

kraken reads its input from standard input, and displays its results on the standard output. For example

kraken < ./data/inputs/balanced-book-1.in.csv

You can use --enable-trade to enable trade matching. Be careful, it has not been as carefully tested, a wild assert could stop your session short.

Architecture

Libraries

The project is divided into small libraries in separate directories, each for a specific purpose:

• book: defines the vocabulary types to quantify orders.
• csv: reading and writing CSV files, in a very naive way.
• engine: the matching engine proper, and a listener interface used to create the expected output.
• parse: parsing the raw CSV data into a list of orders.
• utils: utility types, specifically a StrongType wrapper to ensure a User is not mistaken for a Quantity.

A KISS architecture

In each step of the project, the code was kept to its simplest, trying to solve the problem at hand in the simplest way possible, while keeping to the single responsibility principle. This is why for example:

• The input is parsed at once, and processed in a single step, by different components.
• Almost no efforts were made to avoid superfluous copies, or such optimizations.
• The engine and the expected output are separated from each other through a listener interface, instead of entangling both in the same class.

A test harness

To allow for refactoring without fear, each library has a test-suite to ensure it is in working order.

This allowed me to simplify cancelling orders from having to potentially look at all currently active orders to just a few orders on a given price level.

Reasonably extensible

Given the focus on "events" (the engine processes each order separately, calling the listener at opportune times), it should be fairly simple to extend the core of this code to allow for online processing (i.e: the engine reads its input and displays its output as it comes along), etc...

What I would improve

Matching trades

The logic used when trade matching is enabled is pretty limited: it wasn't clear to me what to do when either of the orders have left-over quantities to be fulfilled. More explicit instructions on this point would lead to the removal of the final FIXMEs and asserts in the code.

I have added explicit test files of those cases in data/invalid.

Picking prices

Another improvement that is specific to trade matching would be scripting the behaviour when bid/ask prices are not exactly equal when matching trades: the current behaviour is to always use the asking price. One could imagine wanting to use bid price, or crossing order price, or the average (weighted by quantity?) of both prices, etc...

Cancelling orders

I do not like the way I have done the cancel_reverse_info_ mapping: to simplify I use a CancelOrder value as a key instead of creating an Engine-specific type.

Repetition

I do not like the repetition that happens due to asks_ and bids_ being "mirror" of each other in the way they should be handled. This is mitigated somewhat by making use of helper lambda functions when the code is identical.

Top of the book handling

I feel like the CallbackOnTopOfBookChange is kind of a hack, even though it was very effective to solve the problem I had of:

• I want to memorize the current top of the book
• At the very end of my current operation, calculate the top of the book again
• Then call the listener back to notify of a change if it happened.

I think there might be a smarter way to go about this. To (mis-)quote Blaise Pascal:

If I had more time, I would have made it shorter.

Complexity analysis

This will focus on the matching engine code, let's discard the complexity of the input pre-processing from this discussion.

Given the use of std::{multi_,}map types, the space analysis is pretty simple: linear with respect to the number of active orders. Empty books are not removed and would therefore also consume a small amount of space: I am not accounting for this in this analysis.

Let's focus on the time complexity.

Flush orders

The simplest to process, we just empty all the book information, in a time complexity linear in the number of active orders in the book.

Cancel order

The first version of this code would have a worst-case cost linear in the number of active orders in the book, simply iterating through each one in turn.

Thanks to a reverse-mapping, the cancel cost is now the following:

• Lookup in cancel_reverse_info_: logarithmic with respect to the number of active orders across all instruments.
• Lookup in bids_/asks_ for the book on a given Symbol: logarithmic with respect to the number of symbols.
• Finding the bounds on the price range: logarithmic with respect to the number of orders in the given book.
• Iterating through that range: linear with respect to the number of orders at the given price range.

Trade order

• Lookup on bids_ and asks_ for the given symbol: logarithmic to the number of symbols.
• Look for a cross of the book, ensure the book is not empty (constant time), and look at the first value in the book: logarithmic to the number of orders in the book
• Inserting the order in the book: logarithmic to the number of orders in the book.
• Inserting into cancel_reverse_info_ (for faster cancelling): logarithmic to the number of orders across all instruments.

Top-of-book handling

For both trade orders and cancel orders, the CallbackOnTopOfBookChange does the following:

• Lookup on bids_ and asks_ for the given symbol: logarithmic to the number of symbols.
• Check the size of the book (constant time) and look at the first order's price: logarithmic to the number of orders in the book.
• Find the price range: logarithmic yet again.
• Iterating on the range: linear to the number of orders at the given price.