Question 1

Which of the following condition is correct if you want to value a European call futures option where the futures price is 50, the strike price is 50, the risk-free rate is 5%, the volatility is 20% and the time to maturity is three months? Show your work in detail. (4 marks)

• 49.38N(0.1)-49.38N(-0.1)
  • 50N(0.05)-50N(-0.05)
  • 49.38N(0.05)-49.38N(-0.05)
  • 48.38N(0.05)-48.38M(-0.05)
  • 50N(0.1)-50N(-0.1)
  • 48.38N(-0.05)-48.38N(0.05)

Question 2 For a European call option on a currency, the exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. How low can the option price be without there being an arbitrage opportunity? (3 marks)

Question 3

The European call and put convexity condition is given below.

Calls (strikes in parentheses): C(90) - 2C(100) + C(110).

Puts (strikes in parentheses): P(90) - 2P(100) + P(110).

Calculate the gross payoffs for the above two portfolios in separate tables if the stock prices are as follows: 70, 80, 90, 100, 110, 120, and 130. What is the relationship between the two portfolios? Explain. Identify what type of spread you get in each case and why? (8 marks)