Make me a market on the number of heads in 100 flips

Question

Interviewer: "A fair coin will be flipped $100$ times. Make me a market on the number of heads. I'll trade either side, one contract settling at the realized count."

Give a bid and ask, and explain what sets your width here versus quoting on, say, the population of a country.

Accepted Answer

Fair value. The count is Binomial(100, 0.5), so the expected number of heads is E[X] = np = 100 \cdot 0.5 = 50. Your fair value is 50, exactly. Key distinction from a "population of Canada" market. When you quote on an unknown fact, your risk is that the counterparty knows the fact and you don't, pure adverse selection, and your width must cover your estimation error. Here the outcome is a future random draw that neither of you can know. There is no informed counterparty, so you can quote tightly around 50; your risk is not being wrong about fair value but the variance of the settlement. What…

Make me a market on the number of heads in 100 flips

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