9. A stock index is trading at 1,544 with r = 1.00% , 9 = 2.00% and volatility at 30.00%. a) Derive an expression for the probability that the index closes at some time T, below a price K. b) Having derived that expression, calculate the numerical value of the probability that that the index closes below 1,544 in one year. 9. A stock index is trading at 1,544 with r = 1.00% , 9 = 2.00% and volatility at 30.00%. a) Derive an expression for the probability that the index closes at some time T, below a price K. b) Having derived that expression, calculate the numerical value of the probability that that the index closes below 1,544 in one year