2. (Time scaling) A stock price S is governed by the model In S(k + 1) = In 5(k)+w(k) where the period length is 1 month. Let v = E[w(k)] and var[w(k)] for all k. Now suppose the basic period length is changed to 1 year Then the model is In S(K1) In S(K) + W(K) where each movement in K corresponds to 1 year What is the natural definition of W(K)? Show that E[W(K)] = 12v and var[W(K)] = 1202 Hence parameters scale in proportion to time.