Consider a certain butterfly spread on AIG stock. 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) Explain, using the fundamental principle, why the butterfly spread must have a positive value now.

(b) 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.

(Fundamental Theorem of Mathematical Finance: If portfolio A is guaranteed to be worth the same (respectively greater than) as Portfolio B at the same time in the future, then its rate is the same now.)