Derivative Contract Fair Price Calculation

Derivative Contract Fair Price Calculation

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Question

You can enter a derivative contract that will pay $100 at the end of a year if the price of oil exceeds $25 per barrel, or $50 if it is equal to $25 or lower. The probability that oil will exceed $25 by the end of one year is 60%. If interest is 4% for one year, what should the fair price of the contract be?

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A. B. C. D.

B

The expected payoff for the contract is $100 * 0.60 + $50 * 0.40 = $80. At 4% interest, the present value of the expected payoff is $80/1.04 = $76.92. A deviation from this value would represent an example of the investment consequences of inconsistent probabilities.

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