QUESTION 1:

a) Explain how a stop-loss hedging scheme can be implemented for the writer of the out-of-money call option. Why does it provide a relatively poor hedge?

b) Plot the payoff patterns of i) a long call position ii) a short put position

c) What are the assumptions of the Black-Scholes model?

d) You observe two European call options on the same asset and the same expiration. The first one has a strike of $140 and a price of $21. The second has a strike of $115 and a price of $35. How can you create a bull spread position? What is the initial cashflow of the strategy? Plot a figure showing how the profit of the bull spread varies depending on the stock price level when the options expire.

e) A stock price is currently at $128. Over the next two one-year periods it is expected to go up by 8% or down by 8% per year. The risk-free rate is 2% per annum. What is the price of a two-year European call option with a strike price of $115?

f) How can you construct a calendar spread using put options? Provide a figure and carefully explain the payoff pattern of the strategy.