Consider a certain butterfly spread on American International Group stock (AIG): this is a portfolio that is long one call at $50, long one call at $70, and short 2 calls at $60. Assume expiration of all options is at the same time t = T . (a) Graph the payoff of this portfolio at expiration T as a function of the stock price ST of AIG. (b) If today the calls cost $13.10, $5.00, and $1.00 for the strikes at 50, 60, and 70, respectively, what will be the profit or loss (PnL) from buying this spread if the stock turns out to be trading at $55 at time T ? at $35? Assume the risk-free rate is 0%. (c) Explain, using the fundamental principle, why the spread must have a positive value now. (Your argument should hold for a general butterfly spread, not just for the special case of premiums given in part (b).) (d) Deduce that the current price of the call with K = 60 is at most the average of the current prices of the other two calls.