5. Consider a Brownian motion W(t) with t > 0 and consider two stock prices de- scribed by Si(t) and S2(t) which fulfill the following stochastic differential equations (SDE) = dSit) usi(t)dt + 01S (t)dW(t) dS 2(t) = M2S 2(t)dt + O2S2(t)dw(t), t0 )t = with ji, M2 E R and 0 2 > 01 > 0. = a) For f(x) = log x, derive the SDE satisfied by the process f(Si(t)). b) Without further calculation, what is the process followed by f(S2(t))? c) Find the SDE satisfied by Y(t) = g(Si(t), S2(t)) = ln(S1(t)/S2(t)) when u = 8 i( Mi = M2. What type of stochastic process is Y(t) undergoing? Describe the parameters of this process. = = [10] 5. Consider a Brownian motion W(t) with t > 0 and consider two stock prices de- scribed by Si(t) and S2(t) which fulfill the following stochastic differential equations (SDE) = dSit) usi(t)dt + 01S (t)dW(t) dS 2(t) = M2S 2(t)dt + O2S2(t)dw(t), t0 )t = with ji, M2 E R and 0 2 > 01 > 0. = a) For f(x) = log x, derive the SDE satisfied by the process f(Si(t)). b) Without further calculation, what is the process followed by f(S2(t))? c) Find the SDE satisfied by Y(t) = g(Si(t), S2(t)) = ln(S1(t)/S2(t)) when u = 8 i( Mi = M2. What type of stochastic process is Y(t) undergoing? Describe the parameters of this process. = = [10]