Which are the order matching algorithms most commonly used by electronic financial exchanges?

Which are the order matching algorithms most commonly used by electronic financial exchanges? Is there a list of order matching algorithms somewhere?

In general, there are two groups of matching algorithms, one for each of the states of the market:

• Continuous trading
• Auction

There's quite a variety of algorithms for auction trading, which is used before the market opens, on market close etc. but most of the time, the markets do continuous trading. I'll therefore go into the latter category here.

The most commonly used ones would be Price/Time priority and Pro-Rata. Both have been adapted and extended for various types of products and use cases, but for brevity, I'll only explain the basics here.

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Price/Time priority, aka FIFO, ensures that

> all orders at the same price level are filled according to time priority; the first order at a price level is the first order matched.

Say the order book, sorted by price and time looks like this:

Id   Side    Time   Qty   Price   Qty    Time   Side  
---+------+-------+-----+-------+-----+-------+------
#3                        20.30   200   09:05   SELL  
#1                        20.30   100   09:01   SELL  
#2                        20.25   100   09:03   SELL  
#5   BUY    09:08   200   20.20                       
#4   BUY    09:06   100   20.15                       
#6   BUY    09:09   200   20.15                       

NB: The order for sorting by time is ascending for buy-side orders and descending for sell-side orders, so that the order with the highest priority is always in the center and priorities decrease outwards (up or down, depending on the side).

Now imagine a new limit order to "buy 250 shares at 20.35" comes in, then it will be filled, in this order:

1. 100 shares at 20.25 (order #2)
2. 100 shares at 20.30 (order #1)
3. 50 shares at 20.30 (order #3)

This leaves the order book in the following state:

Id   Side    Time   Qty   Price   Qty    Time   Side  
---+------+-------+-----+-------+-----+-------+------
#3                        20.30   150   09:05   SELL  
#5   BUY    09:08   200   20.20                       
#4   BUY    09:06   100   20.15                       
#6   BUY    09:09   200   20.15                       

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Pro-Rata ignores the time the orders were placed and allots fill quantities to all orders at a price level according to their relative quantities. Take again the initial order book above, and let us match the same "buy [email protected]" order.

The fills would be:

1. [email protected] (order #2, leaving 150)
2. [email protected] (order #1, 150 x 1/3 = 50)
3. [email protected] (order #3, 150 x 2/3 = 100)

Leaving the following order book like this:

Id   Side    Time   Qty   Price   Qty    Time   Side  
---+------+-------+-----+-------+-----+-------+------
#3                        20.30   100   09:05   SELL  
#1                        20.30    50   09:01   SELL  
#5   BUY    09:08   200   20.20                       
#4   BUY    09:06   100   20.15                       
#6   BUY    09:09   200   20.15                       

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The CME group provides a list of matching algorithms they employ, and links to descriptions of each one.

For more, you might also want to take a look at the "Order matching" related documents on Rajeev's pages.

Generally they use First-In First-Out kinds of algorithms because they maximize the number of effective orders.

Each exchange has its own set of rules which is explained in their websites. This one here is an example.