Question

Suppose that a stock index is currently 900 . The dividend yield is $2 \%$, the risk-free rate is $5 \%$, and the volatility is $40 \%$. Use the results in Technical Note 27 on the author's website to calculate the value of a 1-year average price call where the strike price is 900 and the index level is observed at the end of each quarter for the purposes of the averaging. Compare this with the price calculated by DerivaGem for a 1-year average price option where the price is observed continuously. Provide an intuitive explanation for any differences between the prices.

    Suppose that a stock index is currently 900 . The dividend yield is $2 \%$, the risk-free rate is $5 \%$, and the volatility is $40 \%$. Use the results in Technical Note 27 on the author's website to calculate the value of a 1-year average price call where the strike price is 900 and the index level is observed at the end of each quarter for the purposes of the averaging. Compare this with the price calculated by DerivaGem for a 1-year average price option where the price is observed continuously. Provide an intuitive explanation for any differences between the prices.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 26, Problem 30

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Step 1

The formula for the value of a 1-year average price call option is given by: \[C = e^{-rT} \left( S_0 e^{(r-q)T} N(d_1) - K N(d_2) \right)\] where: - $C$ is the value of the option - $S_0$ is the current index level (900 in this case) - $K$ is the strike Show more…

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Suppose that a stock index is currently 900 . The dividend yield is $2 \%$, the risk-free rate is $5 \%$, and the volatility is $40 \%$. Use the results in Technical Note 27 on the author's website to calculate the value of a 1-year average price call where the strike price is 900 and the index level is observed at the end of each quarter for the purposes of the averaging. Compare this with the price calculated by DerivaGem for a 1-year average price option where the price is observed continuously. Provide an intuitive explanation for any differences between the prices.

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