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Q. 2 (Binomial model gymnastics, 25 pts). Consider an N -period binomial model with up factor u, down factor d, risk-free return r, and probability p ∈ (0, 1) of up. Assume that the principle of no-arbitrage holds in this model. For each n ∈ {0, . . . , N }, let Sn be the stock price at time n. a. (10) Calculate the expected value of Sn. b. (10) Find the distribution of log(Sn). c. (5) What are the expected value and variance of log(Sn)?
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