How The Uncrossing Price Is Computed

During the five-minute pre-open collection window, one stock accumulates this book of limit orders (no trades happen yet — orders just sit there, added, amended, or cancelled freely until the auction fires):

Buy price	Buy shares	Sell price	Sell shares
50.30	400	50.05	500
50.25	600	50.10	600
50.20	800	50.15	900
50.15	500	50.20	400
50.10	700	50.25	700
50.05	300	50.30	300

At the uncrossing instant, the exchange doesn't match these order-by-order in arrival sequence. It runs a specific algorithm, in order of priority:

1. Maximize executed volume. Find the single price at which the most total shares can trade.
2. Minimize surplus imbalance. If more than one price ties for maximum volume, pick whichever leaves the smallest unmatched quantity on one side.
3. Tie-break by reference price. If prices still tie, pick whichever is closest to a designated reference price (typically the last traded price, or the prior close).

Working the book by hand

A buy limit at 50.30 will also transact at any lower price, so the shares "willing to buy at or above" a given price accumulate as price falls. A sell limit at 50.05 will also transact at any higher price, so shares "willing to sell at or below" a given price accumulate as price rises. Building both cumulative columns across the six price levels:

Price	Cumulative buy (≥ price)	Cumulative sell (≤ price)	Matched volume	Imbalance
50.05	3,300	500	500	2,800 buy surplus
50.10	3,000	1,100	1,100	1,900 buy surplus
50.15	2,300	2,000	2,000	300 buy surplus
50.20	1,800	2,400	1,800	600 sell surplus
50.25	1,000	3,100	1,000	2,100 sell surplus
50.30	400	3,400	400	3,000 sell surplus

Matched volume at each price is $\min(\text{cumulative buy}, \text{cumulative sell})$ — you can never trade more than the smaller side offers. Reading down the matched-volume column: 500, 1,100, 2,000, 1,800, 1,000, 400. It rises then falls, peaking at 50.15 with 2,000 shares matched — that is the uncrossing price. No other price gets close: 50.20 only manages 1,800 because cumulative sell interest has already outpaced cumulative buy interest by then.

At the winning price of 50.15, cumulative buy demand is 2,300 and cumulative sell supply is 2,000, so 300 shares of buy interest go unfilled (typically the resting orders with the worst priority — later timestamps or, for pro-rata venues, allocated proportionally). Every filled share, on both sides, prints at exactly 50.15, regardless of whether a given buyer had bid 50.30 or 50.15 — the buyer who bid 50.30 does not pay 50.30, they pay the clearing price, same as everyone else who trades.

When the first rule alone isn't enough

Suppose two neighboring prices had tied at 2,000 matched shares each — say 50.15 and 50.20 both cleared exactly 2,000. Rule 2 looks at leftover imbalance: whichever price leaves fewer unmatched shares on the heavier side wins. If that's also tied, rule 3 takes over — pick whichever tied price is closer to the reference price (commonly the previous close). A prior close of 50.12 would favor 50.15 over 50.20 purely on distance, which also damps artificial swings when the auction book itself is thin.

Where this is used in practice

• Opening and closing crosses. NYSE and Nasdaq run exactly this algorithm at 9:30am and 4:00pm; imbalance figures like the "300 buy surplus" above are published before the auction fires so participants can react.
• Index rebalance and ETF creation/redemption. Funds tracking an index must trade at the closing price, which is why rebalance-day auction volume can run tens of times normal, and why the tie-break rules matter — they set the exact price an entire fund complex settles against.
• Circuit breaker reopenings. After a halt, exchanges typically reopen via a call auction using this same maximize-volume logic rather than resuming continuous trading cold.

In interviews

Be ready to build the cumulative buy and cumulative sell columns from a raw order list under time pressure — that's the actual skill being tested. State the three rules in order (maximize volume, minimize imbalance, tie-break by reference price) and be explicit that matched volume is the minimum of the two cumulative curves, so the answer is wherever that minimum peaks. If asked why exchanges don't just pick the price where demand equals supply exactly, the honest answer is that with discrete order sizes an exact crossing rarely exists — which is why Why Markets Use Call Auctions frames the goal as "maximize trades," not "find equilibrium."