Financial economic question

Consider a special type of lookback option whose payoff at maturity is given by the difference between the maximum and minimum stock prices attained over the life of the option.

LT = max St − min St t∈[0,T ] t∈[0,T ]

Consider pricing this option using the binomial model. Let the current price of stock in Hindsight Inc. be S0 = 216 and consider an option maturing in n = T = 3 periods, so that ∆t = 1 per period. Suppose for the sake of simplicity that the risk free rate is r = 0, and that each period the stock price either doubles u = 2, or fallsbyhalfd=1 =1.

(a) Calculate the risk neutral probability of an uptick p.

  1. (b) (5) An important property of lookback options not shared by vanilla calls and puts is that they are path dependent. That is, their payoffs depend not only on the final stock price but on how the price moved over the life of the option. Show that this option is path dependent, that is, find two price paths that end at the same price.
  2. (c) (15) Draw the stock price tree. Note that there are 2n = 8 possible price paths, in contrast to the n+1 = 4 different final prices.
  3. (d) (15) Using backward induction, calculate the initial price of this option.

I did some work on this 2 question and my friend send me something about, do you want to look at that? Let me share it with you. Its hand written

For this question I think is from lecture 11,12 , I hope this can help you finish early than the deadline and please do not cheat the answer I send to you, and show all detail process(like how to calculate and which formula used)