Let W1(t) and W2(t) be two independent Brownian motion processes. Two stocks evolve according to geometric Brownian motion processes as follows dS1(t)=1S1(t)dt+1S1(t)dW1(t),dS2(t)=2S2(t)dt+2S2(t)dW1(t)+2S2(t)12dW2(t), where [1,1] is the correlation coefficient, i and i for i=1,2 are the instantaneous returns and volatilities of S1(t) and S2(t) respectively. (a) Derive an expression for the variance of S1(t), that is, Var(S1(t)). (b) Use Ito's Lemma to derive the stochastic differential equation for the process Y(t)=S1(t)S2(t). (c) Derive an expression for the covariance between the two stocks, Cov(S1(t),S2(t)). Let W1(t) and W2(t) be two independent Brownian motion processes. Two stocks evolve according to geometric Brownian motion processes as follows dS1(t)=1S1(t)dt+1S1(t)dW1(t),dS2(t)=2S2(t)dt+2S2(t)dW1(t)+2S2(t)12dW2(t), where [1,1] is the correlation coefficient, i and i for i=1,2 are the instantaneous returns and volatilities of S1(t) and S2(t) respectively. (a) Derive an expression for the variance of S1(t), that is, Var(S1(t)). (b) Use Ito's Lemma to derive the stochastic differential equation for the process Y(t)=S1(t)S2(t). (c) Derive an expression for the covariance between the two stocks, Cov(S1(t),S2(t))