In the three-period binomial model with S 0 = 8 , u = 1.25 , d = 0.75 , and 1 + r = 1.2 , consider the American butterfly option that expires at T = 3 and has intrinsic value (for 0 t 3 ) ( S t ) = ( S t 5.5 ) + , S t 8 , ( 10.5 S t ) + , S t 8. (a) Determine the derivative price process and the consumption strategy. Draw a binomial tree showing your findings