Fair value of a call at 30 on two dice multiplied

Question

A contract settles at the product of two fair dice. What should a call on it with strike $30$ cost?

Short answer

$1/6$ . Only a double six (product $36$ ) beats $30$ , paying $6$ with probability $\tfrac1{36}$ , so the fair price is $6/36=\tfrac16$ .

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

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Lessons behind this question

Expectation, Mean, and Variance
Counting and Combinatorics
Conditional Expectation and Variance Revisited

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