Each branch in the tree spans 3 months (5t = 0.25) 60 Node Time: 0.0000 77.04 46.73 0.2500 98.92 60 36.39 0.5000 127.02 77.04 46.73 28.34 163.10 0.7500 98.92 60 36.39 22.07 1.0000 36 of 39 H Let S, S2, S3 and S4 denote the share price at the end of the third, sixth, ninth and twelfth months respectively. An Asian derivative, which expires in 12 months' time, is written on this stock with a payoff function as follows: Le Bach Nguyen Payoff = max (0, 3 (S + S4) - 2 (S + S3)) In words, to calculate the payoff: (i) take the summation of share prices after 6 and 12 months, and multiply by 3, (ii) deduct the summation of share prices after 3 and 9 months, multiplied by 2, (iii) see whether this is bigger than zero. Let "U" denote an up movement on a branch and "D" denote a down movement on a branch. Consider the path DUUD. For this specific path, the payoff to the Asian derivative is OL Consider the path DDDD. For this specific path, the payoff to the Asian derivative is B X 9 ENG US