Question

The spot price of copper is $$\$ 0.60$$ per pound. Suppose that the futures prices (dollars per pound) are as follows: $$ \begin{array}{rr} \hline 3 \text { months } & 0.59 \\ 6 \text { months } & 0.57 \\ 9 \text { months } & 0.54 \\ 12 \text { months } & 0.50 \\ \hline \end{array} $$ The volatility of the price of copper is $40 \%$ per annum and the risk-free rate is $6 \%$ per annum. Use a binomial tree to value an American call option on copper with an exercise price of $$\$ 0.60$$ and a time to maturity of 1 year. Divide the life of the option into four 3-month periods for the purposes of constructing the tree. (Hint: As explained in Section 18.7, the futures price of a variable is its expected future price in a riskneutral world.)

   The spot price of copper is $$\$ 0.60$$ per pound. Suppose that the futures prices (dollars per pound) are as follows:
$$
\begin{array}{rr}
\hline 3 \text { months } & 0.59 \\
6 \text { months } & 0.57 \\
9 \text { months } & 0.54 \\
12 \text { months } & 0.50 \\
\hline
\end{array}
$$
The volatility of the price of copper is $40 \%$ per annum and the risk-free rate is $6 \%$ per annum. Use a binomial tree to value an American call option on copper with an exercise price of $$\$ 0.60$$ and a time to maturity of 1 year. Divide the life of the option into four 3-month periods for the purposes of constructing the tree. (Hint: As explained in Section 18.7, the futures price of a variable is its expected future price in a riskneutral world.)
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Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
John C. Hull 10th Edition
Chapter 21, Problem 19 ↓

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Step 1

The volatility of the price of copper is given as 40% per annum. Since we are dividing the life of the option into four 3-month periods, the volatility for each period is $\frac{40\%}{\sqrt{4}} = 20\%$. The up factor, $u$, is calculated as $e^{(0.20 \times  Show more…

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The spot price of copper is $$\$ 0.60$$ per pound. Suppose that the futures prices (dollars per pound) are as follows: $$ \begin{array}{rr} \hline 3 \text { months } & 0.59 \\ 6 \text { months } & 0.57 \\ 9 \text { months } & 0.54 \\ 12 \text { months } & 0.50 \\ \hline \end{array} $$ The volatility of the price of copper is $40 \%$ per annum and the risk-free rate is $6 \%$ per annum. Use a binomial tree to value an American call option on copper with an exercise price of $$\$ 0.60$$ and a time to maturity of 1 year. Divide the life of the option into four 3-month periods for the purposes of constructing the tree. (Hint: As explained in Section 18.7, the futures price of a variable is its expected future price in a riskneutral world.)
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