European options (calls and puts) on a non-dividend paying stock are available with strike prices of $21, $23,25. The current price of the underlying stock is $23. The price for the calls are $3.5 and $1.5 and 0.5. All those European options (calls and puts) will expire in 6 months. The risk-free interest rate is 10% per annum with continuous compounding. (a) Create a butterfly spread with the European calls, calculate the profit function of the butterfly strategy at the expiration date (2 points) (b) Compute price of the European puts on the same stock with same strike prices and same expiration dates (2 points) (Hint: use put-call parity for European options) (c) Construct another butterfly spread with the European puts and compute the profit function of this second butterfly strategy at the expiration date (2 points) (d) Are the profit functions of those two butterfly spreads same? (1 points)