7.A futures price is currently traded at $95. There is a one-year European call and put options onthe futures with a strike price of $105. The risk-free interest rate is 2% per annum (compounded continuously) and the volatility of the futures is 45% per annum.

(a)What is the value of the call on futures?

(b)What is the value of the put on futures?

8.A stock index currently stands at 100. It is expected to increase by 20% or decrease by 30%over each of the next two time periods of three months. The risk-free interest rate is 3% per annum (compounded continuously) and the dividend yield on the index is 1% per annum (compounded continuously). What is the value of a six-month put option on the index with astrike price of 115 (calculated via two-period binomial option pricing model), if it is

(a)European and

(b)American? Is American put more valuable than European put? Why? In other words, what isyour exercise decision?

9.Currency options: Suppose that the spot price of the Canadian dollar is U.S. $0.95 and that theCanadian dollar-U.S. dollar exchange rate has a volatility of 10% per annum.The risk-free rates of interest in Canada and the United States are 2% and 1% per annum (compounded continuously), respectively.

(a)Calculate the value of a European call option to buy one Canadian dollar for U.S. $0.98 inone year.

(b)Use put-call parity to calculate the European put option to sell one Canadian dollar for U.S.$0.98 in one year.

(c)What is the price of an option to buy U.S. $0.98 with one Canadian dollar in one year?