题目
Assume today's stock price S(0) is $100, the daily log (continuously compounded) return has mean of 0.0 and standard deviation of 0.10 (10%), and tomorrow's stock price is lognormally distributed. What is the approximate probability that tomorrow's stock price will exceed $117.94?
选项
A.about 1%
B.1.43%
C.4.46%
D.about 5%
答案
D
解析
The log return is normally distributed such that LN(117.94/100) =0.165 which is ~N(0,.1).In standard normal units, Z = (0.165 - 0)/0.1 = 1.65.The probability = 1 - CDF = 1 - P[Z<1.65] = 1 - 95% or ~ 5.0% (4.947%). 对数回报的正态分布LN(117.94/100) =0.165LN(117.94/100)=0.165， 即N(0,0.1)正态分布。在标准正态单位中，Z = (0.165 - 0)/0.1 = 1.65 概率= 1-CDF = 1-P[Z<1.65] = 1-95% or ~ 5.0% 4.947%。