Question

A company can buy an option for the delivery of 1 million units of a commodity in 3 years at $$\$ 25$$ per unit. The 3-year futures price is $$\$ 24$$. The risk-free interest rate is $5 \%$ per annum with continuous compounding and the volatility of the futures price is $20 \%$ per annum. How much is the option worth?

   A company can buy an option for the delivery of 1 million units of a commodity in 3 years at $$\$ 25$$ per unit. The 3-year futures price is $$\$ 24$$. The risk-free interest rate is $5 \%$ per annum with continuous compounding and the volatility of the futures price is $20 \%$ per annum. How much is the option worth?

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 36, Problem 5

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Step 1

The delivery price is $25 per unit, and the delivery will happen in 3 years. To calculate the present value of this price, we need to discount it using the risk-free interest rate. PV_delivery_price = $25 * e^(-0.05 * 3) = $25 * e^(-0.15) ≈ $21.67 Show more…

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A company can buy an option for the delivery of 1 million units of a commodity in 3 years at $$\$ 25$$ per unit. The 3-year futures price is $$\$ 24$$. The risk-free interest rate is $5 \%$ per annum with continuous compounding and the volatility of the futures price is $20 \%$ per annum. How much is the option worth?

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