Assume the Black-Scholes framework. For a stock that pays dividends continuously at a rate proportional to its price, you are given: (i) The current stock price is 5. (ii) The stocks volatility is 0.2. (iii) The continuously compounded expected rate of stock-price appreciation is 5%. Consider a 2-year arithmetic average strike option. The strike price is A(2) = { [S(1) +S(2)] Define G = [S(1)S(2)]0.5 . (a) Find the mean and variance of Rt, t+1) for t > 0. (b) Find the mean and variance of R = 0.5[2R(0, 1) +R(1, 2)]. (c) Hence, find the mean and standard deviation of G. (d) Using simulation with 500 trials, estimate the mean of G and (G - 5.5)+. Assume the Black-Scholes framework. For a stock that pays dividends continuously at a rate proportional to its price, you are given: (i) The current stock price is 5. (ii) The stocks volatility is 0.2. (iii) The continuously compounded expected rate of stock-price appreciation is 5%. Consider a 2-year arithmetic average strike option. The strike price is A(2) = { [S(1) +S(2)] Define G = [S(1)S(2)]0.5 . (a) Find the mean and variance of Rt, t+1) for t > 0. (b) Find the mean and variance of R = 0.5[2R(0, 1) +R(1, 2)]. (c) Hence, find the mean and standard deviation of G. (d) Using simulation with 500 trials, estimate the mean of G and (G - 5.5)+