Question

The payoff from a derivative will occur in 8 years. It will equal the average of the 1 -year risk-free interest rates observed at times $5,6,7$, and 8 years applied to a principal of $$\$ 1,000$$. The risk-free yield curve is flat at $6 \%$ with annual compounding and the volatilities of all rates are $16 \%$. Assume perfect correlation between all rates. What is the value of the derivative?

   The payoff from a derivative will occur in 8 years. It will equal the average of the 1 -year risk-free interest rates observed at times $5,6,7$, and 8 years applied to a principal of $$\$ 1,000$$. The risk-free yield curve is flat at $6 \%$ with annual compounding and the volatilities of all rates are $16 \%$. Assume perfect correlation between all rates. What is the value of the derivative?

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 30, Problem 13

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Step 1

The risk-free yield curve is flat at 6% with annual compounding. Therefore, the risk-free interest rate for each year is 6%. To calculate the average interest rate over the 5th, 6th, 7th, and 8th years, we simply take the average of 6% for each year: Average Show more…

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The payoff from a derivative will occur in 8 years. It will equal the average of the 1 -year risk-free interest rates observed at times $5,6,7$, and 8 years applied to a principal of $$\$ 1,000$$. The risk-free yield curve is flat at $6 \%$ with annual compounding and the volatilities of all rates are $16 \%$. Assume perfect correlation between all rates. What is the value of the derivative?

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