Question

Consider an American call option on a stock. The stock price is $$\$ 70$$, the time to maturity is 8 months, the risk-free rate of interest is $10 \%$ per annum, the exercise price is $$\$ 65$$, and the volatility is $32 \%$. A dividend of $$\$ 1$$ is expected after 3 months and again after 6 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Use DerivaGem to calculate the price of the option.

   Consider an American call option on a stock. The stock price is $$\$ 70$$, the time to maturity is 8 months, the risk-free rate of interest is $10 \%$ per annum, the exercise price is $$\$ 65$$, and the volatility is $32 \%$. A dividend of $$\$ 1$$ is expected after 3 months and again after 6 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Use DerivaGem to calculate the price of the option.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 15, Problem 15

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Step 1

The first dividend of $1 is expected after 3 months, so the present value of this dividend is: $$PV_1 = \frac{1}{(1 + r)^{t_1}}$$ where $r$ is the risk-free rate of interest and $t_1$ is the time to the first dividend. Plugging in the values, we get: $$PV_1 = Show more…

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Consider an American call option on a stock. The stock price is $$\$ 70$$, the time to maturity is 8 months, the risk-free rate of interest is $10 \%$ per annum, the exercise price is $$\$ 65$$, and the volatility is $32 \%$. A dividend of $$\$ 1$$ is expected after 3 months and again after 6 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Use DerivaGem to calculate the price of the option.

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