The current stock price is $45 with no expected dividends.  The risk-free rate is 4.00% per year.  The standard deviation for the period in question is 0.4.  The time period is 3 months.  If you are starting from an at-the-money call option formulate a long butterfly spread that also includes a call option that is in-the-money by $5. 

a) Is the resulting butterfly spread symmetrical? Explain why or why not.

b) If you move the call option with the lower strike price to one that is in-the-money by $10, how will that change the butterfly spread?

c) Using the first set of results you got in the very first question, what will the market value of the initial butterfly spread be if the stock price goes up to $55 after one month? Does this result make intuitive sense?  Explain your answer.

d) If you reset the stock price back to $45 and the standard deviation goes down to 0.30, how will that change your answer.Explain why this?