2.1. Suppose that you have a stock in the three-period binomial model with the following param- eters: 1 1 So = 8,1 = ,u = 2, d 4 2 Consider an option whose value at time 3 is the difference between the largest stock price and the smallest stock price among times 0, 1,2,3. That is, V3 = max S- k=0,1,2,3 min Sk k=0,1,2,3 A. Work out the full value tree for (V, V1, V2, V3) for this option. For ease of writing, please use the decimal expansion here for rational numbers that terminate. That is, 6/5=1.2 but not the decimal expansion for numbers like 2/3. B. Suppose that the first coin was tails and the second was heads. At this time (t = 2), how much stock should you own in a replicating portfolio to mimic the payoff of the option? 2.1. Suppose that you have a stock in the three-period binomial model with the following param- eters: 1 1 So = 8,1 = ,u = 2, d 4 2 Consider an option whose value at time 3 is the difference between the largest stock price and the smallest stock price among times 0, 1,2,3. That is, V3 = max S- k=0,1,2,3 min Sk k=0,1,2,3 A. Work out the full value tree for (V, V1, V2, V3) for this option. For ease of writing, please use the decimal expansion here for rational numbers that terminate. That is, 6/5=1.2 but not the decimal expansion for numbers like 2/3. B. Suppose that the first coin was tails and the second was heads. At this time (t = 2), how much stock should you own in a replicating portfolio to mimic the payoff of the option