Make me a market on the product of two dice

Question

Two fair six-sided dice are rolled. A contract pays X \cdot Y in dollars. Compute the fair value exactly and make a two-sided market.

Accepted Answer

Do not enumerate all 36 products. Because the dice are independent, expectation factors: E[XY] = E[X]\,E[Y] = 3.5 	imes 3.5 = 12.25. That is the fair value, exactly 12.25. (You can confirm by summing 	frac{1}{36}\sum{x}\sum{y} xy = 	frac{1}{36}\left(\sum xight)\left(\sum yight) = 	frac{21 	imes 21}{36} = 	frac{441}{36} = 12.25.) The market. Fair = 12.25. Quote for example 11.75 bid, at 12.75. The payoff ranges from 1 (double ones) to 36 (double sixes) and is strongly right-skewed: the median product is much lower than the mean because a single 6 paired with a big number creates rare…

Make me a market on the product of two dice

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