(2) (12 points) Recall the binomial random walk we introduced in class, whereby in any timestep...

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(2) (12 points) Recall the binomial random walk we introduced in class, whereby in any timestep dt the random variable can evolve from S(t) to uS(t) with probability p or to vS(t) with probability 1-p, where u >1 and 0 < v < 1. In class, we solved for u, v, and p in terms of the parameters μ and o², which are related to the mean and variance of the single step probability distribution, using the (arbitrary) constraint that (u 1)S = (1 - v)S. In this problem, please solve for u, v, and p in terms of u and o² (where the meaning of these two parameters is the same as in lecture) but now using the constraint that uv = 1. This constraint means that if the stock price first goes up then comes back down (or vice-versa), it ends at the same price as when it started. Compare your values here to those found in class with the different constraint - how are they similar and how do they differ? - (2) (12 points) Recall the binomial random walk we introduced in class, whereby in any timestep dt the random variable can evolve from S(t) to uS(t) with probability p or to vS(t) with probability 1-p, where u >1 and 0 < v < 1. In class, we solved for u, v, and p in terms of the parameters μ and o², which are related to the mean and variance of the single step probability distribution, using the (arbitrary) constraint that (u 1)S = (1 - v)S. In this problem, please solve for u, v, and p in terms of u and o² (where the meaning of these two parameters is the same as in lecture) but now using the constraint that uv = 1. This constraint means that if the stock price first goes up then comes back down (or vice-versa), it ends at the same price as when it started. Compare your values here to those found in class with the different constraint - how are they similar and how do they differ? -

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To solve for u v and p in terms of and with the constraint uv 1 we can use the following steps 1 Sta... View the full answer