Exam Question The value of an investment asset follows the equation A(t) = exp(Bt), where Bt follows standard Brownian motion. (ii) Calculate the expected value of this investment at time 5. [2] Examiner's Report A(0) = exp(0) = 1, so the students buys 1,000 units of the asset. E[A(5)] = exp(0.5*12 *5) = 12.182 So the expected value of the investment is $12,182 Can someone explain the middle line of the answer above? I am not sure where the 0.5, 12 & 5 come from. Any assistance here would be appreciated.
Hi, I think this is what is happening. B(t) ~ N(0, 1t) B(5) ~ N(0, 5) => A(t) ~ logN(0, 1t) E(A(t)) = exp(mu + 1/2 sigma^2 * t) E(A(t)) = exp(0 + 1/2 1^2 * t) E(A(5)) = exp(1/2 1^2 * 5) = 12.182
