Geometric Brownian Motion. Consider a stock whose price (t) evolves according to a geometric Brownian motion with growth rate v = 5% and volatility O = 20%, that is, s(t) = S(0) ent+oz(t) where r(t) is a standard Wiener process. Compute the expected (total) return of this stock over a period of T = 100 years. Calculate the probability that the return falls short of its expected value. Hint: you can use the following quantiles of a standard normally distributed random variable z. 2 0.00 0.13 0.25 0.39 0.52 0.67 0.84 1.04 1.28 1.64 Prob( 22) 0.50 0.550.600.650.700.750.80 0.85 0.90 0.95 Geometric Brownian Motion. Consider a stock whose price (t) evolves according to a geometric Brownian motion with growth rate v = 5% and volatility O = 20%, that is, s(t) = S(0) ent+oz(t) where r(t) is a standard Wiener process. Compute the expected (total) return of this stock over a period of T = 100 years. Calculate the probability that the return falls short of its expected value. Hint: you can use the following quantiles of a standard normally distributed random variable z. 2 0.00 0.13 0.25 0.39 0.52 0.67 0.84 1.04 1.28 1.64 Prob( 22) 0.50 0.550.600.650.700.750.80 0.85 0.90 0.95