Two-wide market on a dice-product call struck at 19

Question

A contract settles at the product of two fair dice. Consider a call on it with strike $19$ , paying $\max(\text{product}-19,0)$ . You quote a market in the call that is $2$ wide and centred on fair value. Give the bid plus the ask.

Short answer

$19/6$ . Products above $19$ are $20$ (two ways), $24$ (two), $25$ (one), $30$ (two) and $36$ (one), paying $1,5,6,11,17$ . The fair value is $(2+10+6+22+17)/36=19/12$ ; a symmetric market's bid and ask add to twice that.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Counting and Combinatorics
Expectation, Mean, and Variance

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