Problem 4. Assume the lognormal model for stock prices. Stock price today is 40 dollars. Expected total rate of return is 8%. (That means, =0.08 ) Volatility of the stock is 20%. Let S(t) be the stock price at time t. Calculate the following: (a).E[S(3)](b).E[S(3)S(2)=41](c).Cov(ln(S(1)S(4)),ln(S(5)S(8))) Note: In class, we developed the formulas for E[S(t)] and E[S(t2)S(t1)]. Problem 4. Assume the lognormal model for stock prices. Stock price today is 40 dollars. Expected total rate of return is 8%. (That means, =0.08 ) Volatility of the stock is 20%. Let S(t) be the stock price at time t. Calculate the following: (a).E[S(3)](b).E[S(3)S(2)=41](c).Cov(ln(S(1)S(4)),ln(S(5)S(8))) Note: In class, we developed the formulas for E[S(t)] and E[S(t2)S(t1)]