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Edge on a binary contract

Market makingMedium

A contract pays $100$ if an event happens and $0$ otherwise. The event has probability $0.37$ . A market maker sells $12$ units at $40$ . What is the total expected profit?

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Hint

The fair value is probability times payout.

Solution

The fair value is $100 \times 0.37 = 37$ .
The edge per unit sold is $40 - 37 = 3$ .
The total expected profit on $12$ units is $36$ .

Answer: $36$

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