Financial Mathematics

(i) Sketch the graph of the payoff diagram for the following portfolio: long one share, short one European put option with exercise price 100, and short four European call options all with exercise price 80. All options have the same expiry date. [3 marks] (ii) A trader has asked you to construct a portfolio using one call option and one put option with the following requirements: - both options should expire in six months; - the maximum payoff should be attained at ST=50; - the trader is happy to accept large losses if there are large negative or positive movements in the share price. State the portfolio that best fits the requirements and sketch the resulting portfolio