Question

In a 3-month down-and-out call option on silver futures the strike price is $$\$ 20$$ per ounce and the barrier is $$\$ 18$$. The current futures price is $$\$ 19$$, the risk-free interest rate is $5 \%$, and the volatility of silver futures is $40 \%$ per annum. Explain how the option works and calculate its value. What is the value of a regular call option on silver futures with the same terms? What is the value of a down-and-in call option on silver futures with the same terms?

   In a 3-month down-and-out call option on silver futures the strike price is $$\$ 20$$ per ounce and the barrier is $$\$ 18$$. The current futures price is $$\$ 19$$, the risk-free interest rate is $5 \%$, and the volatility of silver futures is $40 \%$ per annum. Explain how the option works and calculate its value. What is the value of a regular call option on silver futures with the same terms? What is the value of a down-and-in call option on silver futures with the same terms?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 26, Problem 19

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Step 1

A down-and-out call option is a type of barrier option that becomes worthless if the underlying asset's price falls below a certain barrier level during the option's lifetime. In this case, the barrier level is $18. Now, let's calculate the value of the Show more…

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In a 3-month down-and-out call option on silver futures the strike price is $$\$ 20$$ per ounce and the barrier is $$\$ 18$$. The current futures price is $$\$ 19$$, the risk-free interest rate is $5 \%$, and the volatility of silver futures is $40 \%$ per annum. Explain how the option works and calculate its value. What is the value of a regular call option on silver futures with the same terms? What is the value of a down-and-in call option on silver futures with the same terms?

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