The current futures price of a stock is $15 per share. One month later, when the futures option expires, the futures price could have risen to $16.5 per share or declined to $14 per share. The strike price is $14.5. The risk-free rate is 6%.

1. What is the value of long futures contract (per share) at the option maturity? (1 mark)

2. To price a futures call option, we construct a risk-free portfolio including a long position consisting of delta shares of futures and a short position on one call futures option. Please solve for delta. (2 marks)

3. What is the value of the risk-free portfolio at the maturity? (1 mark)

4. What is the value of the risk-free portfolio at time zero? (1 mark)

5. What is the cost of futures contract at time zero? (1 mark)

6. Please solve the futures call option premium based on the fact that at time zero, the cost of acquiring a portfolio is equal to the value of the portfolio.

(1 mark)

7. What is the risk neutral probability for pricing the futures option in this case? (2 marks)

8. What is the growth rate of futures prices in risk neutral world? (1 mark)