Assume European options (calls and puts) with strike prices K,,K, = {(K, + K,) and K, are available. The options have the same expiration dates. The underlying stock of the options does not pay dividend. A butterfly spread can be created either using the European calls only or using European puts only. (a) Use the call-put parity to prove that he cost to create the butterfly spread using the European calls are same with the cost to create the butterfly spread using the European puts (2 points) (b)Prove that profit function of the butterfly spread created using the European calls is same with the profit function of the butterfly spread created using the European puts. The profit function referred here is the profit function of the butterfly spread at the expiration time. (2 points)