question archive Suppose that a stock price s follows geometric Brownian motion with ex- pected return u and volatility o: dS = u Sat +oSdz
Suppose that a stock price s follows geometric Brownian motion with ex- pected return u and volatility o: dS = u Sat +oSdz
Subject:FinancePrice:2.86 Bought9
Suppose that a stock price s follows geometric Brownian motion with ex- pected return u and volatility o: dS = u Sat +oSdz. (16) Define the process F as: F = S" (17) and its logarithm as: f = log(F), (18) where n is some constant. (a) [20 marks] What is the process followed by the variable F = Sn? (b) [20 marks] Show that F also follows geometric Brownian motion. (c) [20 marks] Find the law of motion equation df. Show the intermediate steps. (d) [40 marks] Suppose that in the first two years H = 2 and 0 = 3 and for the next two years u = 3 and 0 = 4. If the initial value of the variable is So = 2 and n=1 find: i. the expected value of S and F = Safter two years; ii. the probability distribution of f2 - fo; iii. the probability distribution of f4 – fo; iv. the probability distribution of fa.
