Question

Consider an American call option on a stock. The stock price is $$\$ 50$$, the time to maturity is 15 months, the risk-free rate of interest is $8 \%$ per annum, the exercise price is $$\$ 55$$, and the volatility is $25 \%$. Dividends of $$\$ 1.50$$ are expected in 4 months and 10 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Calculate the price of the option.

   Consider an American call option on a stock. The stock price is $$\$ 50$$, the time to maturity is 15 months, the risk-free rate of interest is $8 \%$ per annum, the exercise price is $$\$ 55$$, and the volatility is $25 \%$. Dividends of $$\$ 1.50$$ are expected in 4 months and 10 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Calculate the price of the option.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 15, Problem 21

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Step 1

The first dividend of $$\$ 1.50$$ is expected in 4 months, so the present value of this dividend is: $$PV_1 = \frac{1.50}{(1+0.08)^{\frac{4}{12}}} = \$1.46$$ Similarly, the second dividend of $$\$ 1.50$$ is expected in 10 months, so the present value of this Show more…

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Consider an American call option on a stock. The stock price is $$\$ 50$$, the time to maturity is 15 months, the risk-free rate of interest is $8 \%$ per annum, the exercise price is $$\$ 55$$, and the volatility is $25 \%$. Dividends of $$\$ 1.50$$ are expected in 4 months and 10 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Calculate the price of the option.

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