Question

A stock price is currently $$\$ 30$$. During each 2-month period for the next 4 months it will increase by $8 \%$ or reduce by $10 \%$. The risk-free interest rate is $5 \%$. Use a two-step tree to calculate the value of a derivative that pays off $\left[\max \left(30-S_T, 0\right)\right]^2$, where $S_T$ is the stock price in 4 months. If the derivative is American-style, should it be exercised early?

   A stock price is currently $$\$ 30$$. During each 2-month period for the next 4 months it will increase by $8 \%$ or reduce by $10 \%$. The risk-free interest rate is $5 \%$. Use a two-step tree to calculate the value of a derivative that pays off $\left[\max \left(30-S_T, 0\right)\right]^2$, where $S_T$ is the stock price in 4 months. If the derivative is American-style, should it be exercised early?

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 13, Problem 24

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Step 1

We have two possibilities: an increase of $8 \%$ or a decrease of $10 \%$. For an increase of $8 \%$, the stock price in 4 months would be $30 \times (1 + 0.08) = 32.4$. For a decrease of $10 \%$, the stock price in 4 months would be $30 \times (1 - 0.10) = Show more…

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A stock price is currently $$\$ 30$$. During each 2-month period for the next 4 months it will increase by $8 \%$ or reduce by $10 \%$. The risk-free interest rate is $5 \%$. Use a two-step tree to calculate the value of a derivative that pays off $\left[\max \left(30-S_T, 0\right)\right]^2$, where $S_T$ is the stock price in 4 months. If the derivative is American-style, should it be exercised early?

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