Consider that the stock price follows an Ornstein Uhlenbeck process. It is a solution to the SDE: dS(t) = [a+bS(t)]dt +odW(t) where a, b, o are some constants and b + 0 (a) Apply Ito's lemma to obtain the solution to the SDE. (b) What are the mean and the variance of the stock price? (c) Derive the general equation of the probability when the stock price is negative at time t > 0. (d) Suppose that S(0) = 5, a = 2, b = 20% and o 20. Compute the probability that the stock price is negative at t = 5. Consider that the stock price follows an Ornstein Uhlenbeck process. It is a solution to the SDE: dS(t) = [a+bS(t)]dt +odW(t) where a, b, o are some constants and b + 0 (a) Apply Ito's lemma to obtain the solution to the SDE. (b) What are the mean and the variance of the stock price? (c) Derive the general equation of the probability when the stock price is negative at time t > 0. (d) Suppose that S(0) = 5, a = 2, b = 20% and o 20. Compute the probability that the stock price is negative at t = 5