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Question 1 ( H17.12)

A futures price is currently 60 and its volatility is 30%. The risk-free interest rate is

8% per annum. Use a two-step binomial tree to calculate the value of a six-month European call option on the futures with a strike price of 60? If the call were American, would it ever be worth exercising it early?

Question 2 (H17.7)

Calculate the value of a five-month European put futures option when the futures

price is $19, the strike price is $20, the risk-free interest rate is 12% per annum, and the volatility of the futures price is 20% per annum.

Question 3 (H16.16)

Suppose that a portfolio is worth $60 million and the S&P 500 is at 1200. If the value of the portfolio mirrors the value of the index, what options should be purchased to provide protection against the value of the portfolio falling below $54 million in one year’s time?

Question 4 (H16.17)

Consider again the situation in Problem 16.16. Suppose that the portfolio has a beta

of 2.0, the risk-free interest rate is 5% per annum, and the dividend yield on both the portfolio and the index is 3% per annum. What options should be purchased to provide protection against the value of the portfolio falling below $54 million in one year’s time?

Question 5 (H25.19)

In a three-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?

Question 6 (H25.11)

Explain why delta hedging is easier for Asian options than for regular options.