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Market makingMedium

Venue A offers to sell $30$ units at $100$ and $50$ units at $100.3$ . Venue B offers to buy $20$ units at $100.5$ and $40$ units at $100.2$ . A trader buys from A and sells to B, taking every trade that has a positive profit and matching the best prices first. What is the total profit?

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Hint

Pair the cheapest offers with the highest bids until the gap closes.

Solution

The first $20$ units are bought at $100$ and sold at $100.5$ , earning $20 \times 0.5 = 10$ .
The next $10$ units are bought at $100$ and sold at $100.2$ , earning $10 \times 0.2 = 2$ .
The next offer at $100.3$ is above the remaining bid at $100.2$ , so the total profit is $12$ .

Answer: $12$

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