The diagram below depicts a 4-step Binomial tree to model share price. Each branch in the tree spans 3 months (St = 0.25). 222.55 182.21 149.18 149.18 122.14 122.14 100 100 100 81.87 81.87 67.03 67.03 54.88 44.93 Node Time 0.0000 0.2500 0.5000 0.7500 1.0000 Let S1, S2, S3 and S4 denote the share price at the end of the third, sixth, ninth and twelfth months respectively. An'average rate' Asian derivative, which matures in 12 months' time, is written on this stock with a payoff function as follows: Payoff = max(0,3(S, +S4)-1(S,+S)) In words, to calculate the payoff to the derivative: (i) take the average of the share prices after 9 and 12 months, (ii) deduct the average of the share prices after 3 and 6 months, (iii) see whether this is bigger than 0. Consider the path UDDU. For this specific path, the payoff to the Asian derivative is Consider the path UUUD. For this specific path, the payoff to the Asian derivative is The diagram below depicts a 4-step Binomial tree to model share price. Each branch in the tree spans 3 months (St = 0.25). 222.55 182.21 149.18 149.18 122.14 122.14 100 100 100 81.87 81.87 67.03 67.03 54.88 44.93 Node Time 0.0000 0.2500 0.5000 0.7500 1.0000 Let S1, S2, S3 and S4 denote the share price at the end of the third, sixth, ninth and twelfth months respectively. An'average rate' Asian derivative, which matures in 12 months' time, is written on this stock with a payoff function as follows: Payoff = max(0,3(S, +S4)-1(S,+S)) In words, to calculate the payoff to the derivative: (i) take the average of the share prices after 9 and 12 months, (ii) deduct the average of the share prices after 3 and 6 months, (iii) see whether this is bigger than 0. Consider the path UDDU. For this specific path, the payoff to the Asian derivative is Consider the path UUUD. For this specific path, the payoff to the Asian derivative is