Question

A 6-month American call option on a stock is expected to pay dividends of $$\$ 1$$ per share at the end of the second month and the fifth month. The current stock price is $$\$ 30$$, the exercise price is $$\$ 34$$, the risk-free interest rate is $10 \%$ per annum, and the volatility of the part of the stock price that will not be used to pay the dividends is $30 \%$ per annum. Use the DerivaGem software with the life of the option divided into six time steps to estimate the value of the option. Compare your answer with that given by Black's approximation (see Section 15.12).

   A 6-month American call option on a stock is expected to pay dividends of $$\$ 1$$ per share at the end of the second month and the fifth month. The current stock price is $$\$ 30$$, the exercise price is $$\$ 34$$, the risk-free interest rate is $10 \%$ per annum, and the volatility of the part of the stock price that will not be used to pay the dividends is $30 \%$ per annum. Use the DerivaGem software with the life of the option divided into six time steps to estimate the value of the option. Compare your answer with that given by Black's approximation (see Section 15.12).

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 21, Problem 27

Instant Answer

Step 1

First, we need to calculate the ex-dividend dates. The dividends are paid at the end of the second and fifth months, so the ex-dividend dates are at the beginning of the third and sixth months. Show more…

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A 6-month American call option on a stock is expected to pay dividends of $$\$ 1$$ per share at the end of the second month and the fifth month. The current stock price is $$\$ 30$$, the exercise price is $$\$ 34$$, the risk-free interest rate is $10 \%$ per annum, and the volatility of the part of the stock price that will not be used to pay the dividends is $30 \%$ per annum. Use the DerivaGem software with the life of the option divided into six time steps to estimate the value of the option. Compare your answer with that given by Black's approximation (see Section 15.12).

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