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Skewed market edge

Market makingMedium

A contract is worth $100$ . A market maker quotes a bid of $98$ and an ask of $104$ . The next order is equally likely to be a buy at the ask or a sell at the bid, and it trades one unit. What is the market maker's expected profit on that order relative to fair value?

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Hint

Compute the edge on each side, then weight by probability.

Solution

If the order buys at the ask, the edge is $104 - 100 = 4$ .
If the order sells at the bid, the edge is $100 - 98 = 2$ .
The expected edge is $0.5 \times 4 + 0.5 \times 2 = 3$ .

Answer: $3$

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