Make a market on the sum of ten dice

Question

Interviewer: "I roll ten fair six-sided dice and add them up. Make me a market on the total. I will trade either side, one contract settling at the realized sum."

Give a bid and ask, and explain what determines your width.

Accepted Answer

Fair value. One die has expected value \frac{1+2+\cdots+6}{6} = 3.5. Ten independent dice add linearly: E[	ext{total}] = 10 \cdot 3.5 = 35. Your fair value is 35, exactly. This is a future random draw, not an unknown fact, so no counterparty can know the outcome in advance: there is no adverse selection. You can quote tightly around 35. What sets the width. The variance of the settlement. One die has variance \frac{6^2 - 1}{12} = \frac{35}{12} \approx 2.92. For ten independent dice, variances add: 	ext{Var}(	ext{total}) = 10 \cdot \frac{35}{12} = \frac{350}{12} \approx 29.2, \qquad \sigma …

Make a market on the sum of ten dice

Your answer

More Market Making questions