Demonstrate that for a continuum of call prices concave in strike over the region [K1,K2], a butterfly spread consisting of a long call struck at K1, a long call struck at K2 and two short calls struck at (K1 +K2)/2 will always make money for the seller. Discuss the meaning of the arbitrage in terms of the implied probability distribution of the stock at the relevant maturity. (This is referred to as butterfly spread arbitrage.)