Let S(0) 100, R = 0.05, U = 0.2, D = -0.2, and N = 3, and consider the payoff of following European butterfly spread: -30- -20- -10- 50 = 60 70 80 90 100 110 120 130 140 (a) You can construct this spread by buying and/or selling European call options. List the call options needed to replicate the butterfly spread. (b) Price the butterfly spread by taking the discounted risk-neutral ex- pected value off the option payoff. (c) Price the four call options from part (a) using your program. What is the sum of the call options? (remember to adjust the sign based on whether you are buying or selling) (d) Draw the gain of butterfly spread.