8. Consider a stock currently trading at S = 80 whose price evolution can be represented by a binomial tree with parameters u = 1.226 and d = 0.815. Suppose the per-period gross rate of interest is R = 1.005.
(a) Price a one-period call option on the tree with a strike of K = 76.
(b) Using backwards induction, find the price of a forward start call option that comes to life in one period, has a further life of one period, and has a strike equal to 95% of the stock price when it comes to life. Verify that it is the same as your answer to (a).
(c) Find the initial delta of the forward start.
(d) Now assume that the initial stock price is S = 1. Assuming the same parameters for the binomial tree, find the price of a one-period call with strike K = 0.95. How does this price compare to the delta you identified in part (c)? Why?
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