(a) Sketch a plot for a European put option at expiry, assuming the final value of the share is always $30, as a function of the strike price which varies between $0 and $80. (3 marks) (b) Consider an option to buy a share, in months time, for $X, assuming the current value of the share is $S0, the volatility of the share is , and the risk-free interest rate is r% per month. Determine the value of the option if S0=Xe(r+2/2). Please show full working. (5 marks) (c) What is the value of an option to buy a share, in one years time, for $X, assuming the current value of the share is $127,X127 (i.e. X is so much lower than 127 that we can ignore the possibility of the share falling to X ), and the risk-free interest rate is 7% per year? Explain a strategy, involving no trading, which can realise this value without risk. You may assume that short selling of shares is allowed, with no brokerage fee, and money can be borrowed or invested at the risk-free interest rate without risk. Please show full working. (6 marks) (d) You have just been issued 200 shares which you must continue to hold for three months, 150 shares which you must continue to hold for six months, and another 250 shares which you must continue to hold for one year. Assuming you can buy and/or sell put and call options in the shares, at a variety of strike prices and for durations of 3 months, 6 months, and of one year, explain a strategy that you should use to lock in the current value of the shares, i.e. to eliminate any risk from their value falling (or rising)? Include in your explanation how the strategy will work in the event the share price increases and in the event the share price decreases. (6 marks)