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J.P. Morgan Intern Interview Question

"We play a game, where you roll a dice, and I pay you the value of the roll. What is the price you would pay to play this game with me? What about if I gave you the option to roll a second time?"
Tags: option pricing
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The fair price for one roll is 3.5, as this is the expected value.
If you get another roll, you will only use it if you score a 1, 2 or 3 on the next, seeing as otherwise, you have already exceeded your expectation.
Thus, half the time you roll a 4, 5 or 6 on the first roll. This has expectation 5.
The other half of the time, you roll a 1, 2 or 3 on the first roll. You then roll again, and the second roll has expectation 3.5.
So, half the time we get 5, and half the time 3.5. The fair price is now 4.25.

- Interview Candidate on Sep 17, 2012

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