{2) (12 points) Recall the binomial random wall: we introduced in class, whereby in any timestep t the random variable can evolve from S{t) to 11.3(t) with probability j') or to T3313) with probability 1 p, where a. I} 1 and [l {I 1: =1 1. In class, we solved for a, 1-1, and p in terms of the parameters ,u and .272, which are related to the mean and variance of the single step probability distribution, using the (arbitrary) constraint that (a. 1qu = (1 1:)3. In this problem, please solve for a} w, and p in terms of Is, and 0'2 {where the meaning of these two parameters is the same as in lecture} but now using the constraint that as = 1. This constraint means that if the stock price rst goes up then comes back down [or vice-verse}, it ends at the same price as when it started, regardless of what 3 was originally [the constraints from class do not do this}. Compare your values for u, a, and 33 here to those found in class with the different constraint - how are they similar and how do they differ? Specically focus on what happens at {it > I] by comparing the Taylor polynomials for the wn'ious formulas in terms of power of t