Question

A 1-year American put option on a non-dividend-paying stock has an exercise price of $$\$ 18$$. The current stock price is $$\$ 20$$, the risk-free interest rate is $15 \%$ per annum, and the volatility of the stock price is $40 \%$ per annum. Use the DerivaGem software with four 3 -month time steps to estimate the value of the option. Display the tree and verify that the option prices at the final and penultimate nodes are correct. Use DerivaGem to value the European version of the option. Use the control variate technique to improve your estimate of the price of the American option.

   A 1-year American put option on a non-dividend-paying stock has an exercise price of $$\$ 18$$. The current stock price is $$\$ 20$$, the risk-free interest rate is $15 \%$ per annum, and the volatility of the stock price is $40 \%$ per annum. Use the DerivaGem software with four 3 -month time steps to estimate the value of the option. Display the tree and verify that the option prices at the final and penultimate nodes are correct. Use DerivaGem to value the European version of the option. Use the control variate technique to improve your estimate of the price of the American option.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 21, Problem 13

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Step 1

You have the following inputs: - Current stock price ($S_0$) = \$20 - Exercise price ($K$) = \$18 - Risk-free interest rate ($r$) = 15% per annum - Volatility ($\sigma$) = 40% per annum - Time to maturity ($T$) = 1 year - Number of time steps Show more…

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A 1-year American put option on a non-dividend-paying stock has an exercise price of $$\$ 18$$. The current stock price is $$\$ 20$$, the risk-free interest rate is $15 \%$ per annum, and the volatility of the stock price is $40 \%$ per annum. Use the DerivaGem software with four 3 -month time steps to estimate the value of the option. Display the tree and verify that the option prices at the final and penultimate nodes are correct. Use DerivaGem to value the European version of the option. Use the control variate technique to improve your estimate of the price of the American option.

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