We try to model an asset with price St at time t = 0,1,2,3,4. Today, S0 = 10. For each case A, B, C below, answer the following questions:
i) What are the possible values of S4 within this model?
ii) What is the expected mean and variance of S4?
A) Random Walk model: Suppose that prices can go either up $1 or down $1 each period. Assume that the probability of an up-move is 0.55 at each step, independently of everything else.
B) Trinomial Tree model: suppose that prices can evolve in one of the following 3 ways: { go up $1 with prob.0.4, stay ?at with prob.0.3, go down $1 with prob.0.3}
C) Binomial Tree: suppose that each period prices either go up by 10% with probability 0.55, or down by 10% with prob. 0.45.