91Ó°ÊÓ

A futures price is currently \(70,\) its volatility is \(20 \%\) per annum, and the risk-free interest rate is \(6 \%\) per annum. What is the value of a five- month European put on the futures with a strike price of \(65 ?\)

Suppose that a one-year futures price is currently \(35 .\) A one-year European call option and a one-year European put option on the futures with a strike price of 34 are both priced at 2 in the market. The risk-free interest rate is \(10 \%\) per annum: Identify an arbitrage opportunity.

Suppose that a futures price is currently \(30 .\) The risk-free interest rate is \(5 \%\) per annum. A three-month American call futures option with a strike price of 28 is worth 4 Calculate bounds for the price of a three-month American put futures option with a strike price of 28

Calculate the price of a three-month European call option on the spot value of silver. The three-month futures price is \(\$ 12,\) the strike price is \(\$ 13,\) the risk-free rate is \(4 \%\) and the volatility of the price of silver is \(25 \%\)

A futures price is currently \(40 .\) It is known that at the end of three months the price will be either 35 or \(45 .\) What is the value of a three- month European call option on the futures with a strike price of 42 if the risk-free interest rate is \(7 \%\) per annum?

Calculate the implied volatility of soybean futures prices from the following information concerning a European put on soybean futures: $$\begin{array}{ll} \hline \text { Current futures price } & 525 \\ \text { Exercise price } & 525 \\ \text { Risk-free rate } & 6 \% \text { per annum } \\ \text { Time to maturity } & 5 \text { months } \\ \text { Put price } & 20 \\ \hline \end{array}$$

Calculate the price of a six-month European put option on the spot value of the S\&P 500 . The six-month forward price of the index is 1,400 , the strike price is 1,450 , the risk-free rate is \(5 \%,\) and the volatility of the index is \(15 \%\)