You are an arbitrageur looking for opportunities to capitalise on mispriced securities. You notice that the BHP put option, expiring on the 26th November 2010, with an exercise price of $46 may be mispriced. You calculated the historical volatility is 21.27%.Today's date is the 1st of October. The current stock price for BHP is $40.74.

a) Demonstrate why you believe the option is mispriced and develop a strategy to take advantage of the mispricing, assume you are correct with your estimate of historical volatility.

b) Show the risk-free portfolio that you have developed and calculate the profit that you will make if price of the option reverts to your expected theoretical value in the same day without anything else changing.

c) Soppose the mispricing of the put option is not corrected on same day. Explain what actions you would take to ensure your arbitrage portfolio remains risk free, what additional consideration need to be made?

d) You believe that there will be a series of unexpected earnings announcements in the coming weeks, while continuing to ensure your risk free position is maintained from part (a) , demonstrate how the portfolio can be altered to maximise the profit from this information.

e) On the 20 Nov, BHP will release its earning figures for the quarter ending 30th Oct 2010.Suppose the market expects the earning figure to be in line with the projections in the company's financial statement. However, you believe that due to a lack of demand from China. Commodity prices are fail, especially for resources such as nickel and iron.Would you be prefer to be long or short on the put option (X=$46) mentioned in part a? If other market participants have the same view, what effect would this have on the volatility skew?