Simulating Pro-Rata Matching

Most equity exchanges fill resting orders price-then-time: at the best price, whoever arrived first gets filled first. Some markets — many futures and options exchanges in particular — instead use pro-rata matching at the best price: an incoming order is split across all resting orders at that price in proportion to their size, regardless of who arrived first. A backtest that assumes time priority everywhere will badly misjudge fill rates and adverse selection on a pro-rata venue, so the simulator needs a matching rule that mirrors the real one.

Simulating this means, for every incoming order, identifying all resting orders at the matched price, computing each one's share of the fill as its size divided by the total resting size at that price (subject to the exchange's own rounding and minimum-fill rules), and allocating fills accordingly rather than walking the queue in arrival order.

Worked example

Three resting buy orders sit at the best bid: 100, 300, and 600 contracts, a total of 1,000. A sell order for 200 contracts arrives. Pro-rata allocates each resting order its proportional share: $100/1000 \times 200 = 20$, $300/1000 \times 200 = 60$, and $600/1000 \times 200 = 120$ contracts respectively. A simulator using time priority instead would have filled the first order for its full 100 and moved on — a completely different, and wrong, outcome for a pro-rata venue.