Problem 4 (a) A stock price S is governed by the model In S(k 1)- In S(k) +w(k) where the period length is 1 month. Let v Elo(k)] and 2-var[w(k)] for all k. Now suppose the basic period length is changed to 1 year. Then the model is InS(K 1)- InS(K)+W(K) where each movement in K corresponds to 1 year. What is the natural definition of W(K)? Show that ElW(K)]-12v and var(W(K)-122. Hence parameters scale in proportion to time. (b) A stock price S is governed by ds - aSdt bSdz where z is a standardized Wiener process. Find the process that governs Gu)-s) Problem 4 (a) A stock price S is governed by the model In S(k 1)- In S(k) +w(k) where the period length is 1 month. Let v Elo(k)] and 2-var[w(k)] for all k. Now suppose the basic period length is changed to 1 year. Then the model is InS(K 1)- InS(K)+W(K) where each movement in K corresponds to 1 year. What is the natural definition of W(K)? Show that ElW(K)]-12v and var(W(K)-122. Hence parameters scale in proportion to time. (b) A stock price S is governed by ds - aSdt bSdz where z is a standardized Wiener process. Find the process that governs Gu)-s)