Consider two strategies formed from a combination of options, which all have the same one-year maturity and are written on the same stock. The firm does not pay dividends.

Strategy A: Long a call (C1) with 1 = $40 and long a put (P1) with X2 = $60 Strategy B: Long a put (P2) with 1= $40 and long a call (C2) with 2 = $60

A. (5 marks) Which strategy would you choose if the two strategies have the same costs? Explain your answer. Hint: Draw the payoff diagrams.

You now collect more information about the available securities. You find that the current stock price is $55 and the current risk-free rate is 0.5% p.a. . The price of both C1 and P1 give the same implied volatility of 40% per annum for the stock.

B. (5 marks) Calculate the cost of Strategy A using the Black-Scholes formula.

You believe that the implied volatility on the stock as suggested by the price of the options is an inaccurate measure of the true volatility of the stock. You have built a more sophisticated model for volatility that predicts that the stocks true volatility is 50% p.a..

C. (6 marks) You wish to capitalise on the perceived mispricing of the options written on this stock by holding a delta-neutral portfolio consisting only of positions in the underlying stock and in put option P1 as described in Strategy A. Will you buy or sell P1? If you take 1000 positions in the put (long or short), what position will you take in the shares (how many shares will you trade and in what direction)? What would be the approximate profit of the delta-neutral portfolio if the markets assessment of volatility quickly corrects to your own better estimate? Show all of your portfolio construction steps and the calculations to capture the profits.

D. (4 marks) What are the risks of your delta-neutral strategy in Part C?