1. A European call option is written on company As shares. The exercise price is $3.50. The current share price of company is 3.9 and the annual standard deviation of the shares is 20% (0.2) pa. The risk-free rate is 3% pa continuously compounded and the option expiry date is six months from the present. Calculate the theoretical value of the call option using the Black-Scholes model. (3 marks)
2. You have a portfolio of 5M shares of Firm A. The market price of each share of Firm A is equal to $5. You are worried about the potential for shares to decline rapidly, resulting in large losses. Explain how you can use options to hedge your downside risk with Firm A, whilst maintaining your ability to profit if Firm As share price rises. Use a numerical example to demonstrate your strategy. (Hint: A payoff diagram might assist). (3 marks)
3. Instead of hedging the downside risk of your portfolio of 5M stocks of Firm A you would like to increase by three times your gains above the stock price of $6. How can you achieve this by using options? (2 marks)