(10 pts) Consider that the 6-month effective interest rate is 2%, the S&R 6-month forward price is 1020 and the current index price is 1000. No dividend is paid in this period. The premiums of some S&R European options with 6-month to expiration are given below: Strike 950 1050 Call 120.405 71.802 Put 51.777 101.214 Derive the profit function (in terms of S0.5) and draw the corresponding diagram for the following positions at the end the the sixth month. (a) Long one share of S&R index and long a 950-strike put. (b) Long a 950-strike call and short two 1050-strike calls