Value of a Dice Option

What this expected-value option-pricing interview question tests

This is a medium-difficulty probability problem commonly used to screen candidates for quantitative trading and finance roles. It combines expected value calculation with optimal decision-making under uncertainty—specifically, the idea that the holder of an option will exercise it only when doing so increases their payoff.

To solve problems like this, you need to work backwards from the decision point. Once you observe your first roll, you must decide whether exercising the option (rolling again) is worth it. This requires computing the conditional expected value of a second roll and comparing it to the value you already hold. Then, knowing how you will optimally behave at each future state, you can calculate the fair price today.

• Conditional expectation and the law of total expectation
• Optimal stopping and exercise decisions
• Backward induction through a decision tree