How orders are matched: price-time priority and auctions

What you will learn

• How price-time priority decides which resting order trades first.
• At which price an incoming order trades, and when it gets price improvement.
• How pro-rata allocation differs from time priority.
• How to calculate an auction price step by step from a list of orders.

Explanation

A matching engine is the venue software that matches incoming and resting orders under fixed, published rules. Auction schedules were covered in the course "Stocks" and return in lesson 8; here we look at the calculation.

Continuous trading: price-time priority

Under price-time priority, the engine ranks resting orders:

1. Price first: a higher bid ranks before a lower bid; a lower ask ranks before a higher ask.
2. Time second: at the same price, the order that arrived earlier trades first. This is your place in the queue.

On Xetra, market orders rank ahead of limit orders. Changing an order's price or increasing its size usually gives it a new timestamp; reducing the size usually does not.

Which price?

A trade in continuous trading takes place at the price of the resting order. If you send a buy limit at €20.03 and the best ask is €20.02, you buy at €20.02, one cent better than your limit. This is price improvement compared with your limit.

In a partial fill, the untraded rest stays in the book or is cancelled, depending on time-in-force.

Pro-rata allocation

Some futures markets, mainly for certain interest-rate contracts, use pro-rata allocation instead: an incoming order is split among all resting orders at the best price in proportion to their size. Size matters more than speed; some venues combine both methods.

Auctions

In an auction, orders are collected during a call phase without trading. The venue usually shows an indicative price. On Xetra, the call phase ends at a random moment within a short period, so nobody can place a last-second order with certainty. Then the engine determines one single price at which all executed orders trade (uncrossing).

The Xetra rules, in order:

1. Choose the price with the highest executable volume.
2. If several prices tie, choose the one with the lowest surplus (unmatched volume at that price).
3. If they still tie: if the surplus is on the buy side at all of them, take the highest price; if it is on the sell side at all, take the lowest.
4. Otherwise the reference price (last traded price) decides: if it is at or above the highest candidate, use the highest; at or below the lowest, use the lowest; in between, use the reference price.

For each candidate price, demand = market buy orders + buy limits at or above that price; supply = market sell orders + sell limits at or below it. Executable volume = the smaller of the two.

Worked example

Hypothetical example 1 (continuous): two asks rest at €20.02: order A, 300 shares (entered first), and order B, 500 shares. You send a buy limit at €20.03 for 600 shares. Result: 300 from A at €20.02, then 300 from B at €20.02. B keeps 200 shares in the book. Price improvement: €0.01 × 600 = €6.00 compared with your limit.

Pro-rata: resting orders of 600 and 400 shares at the best price, incoming order 500: 500 × 600/1,000 = 300 and 500 × 400/1,000 = 200.

Hypothetical example 2 (auction): market buy 100, market sell 100, plus these limits.

Check at €10.03: demand = 100 + 300 + 200 + 400 = 1,000; supply = 100 + 200 + 300 + 300 = 900. The highest executable volume, 900 shares, is reached only at €10.03, so the auction price is €10.03. All 900 shares trade at €10.03, even for buyers whose limit was €10.05. The buy limits at €10.03 receive only 300 of their 400 shares. Exclusions: fees.

Common mistake

Practice activity

Hypothetical auction with no market orders. Buy limits: €5.10 × 400, €5.09 × 300, €5.08 × 500, €5.07 × 600. Sell limits: €5.07 × 300, €5.08 × 400, €5.09 × 500, €5.10 × 600. The reference price is €5.12.

1. Calculate demand, supply, executable volume and surplus at each price.
2. Determine the auction price using the rules above.

Key takeaways

• Continuous trading ranks orders by price first and time second; trades happen at the resting order's price.
• Pro-rata allocation rewards size instead of speed and is used in some futures markets.
• An auction picks the price with maximum executable volume, then minimum surplus, then the tie-break rules.
• Everyone executed in an auction trades at the same price.

Next step

The next lesson turns to the cost of execution: slippage and market impact, with worked numbers.