题目
A stock is priced at $100.00 and follows a one-period binomial process with an up move that equals 1.05 and a down move that equals 0.97. If 1 million Bernoulli trials are conducted, and the average terminal stock price is $102.00, the probability of an up move （ ） is closest to:
选项
A.0.375.
B.0.500.
C.0.625.
答案
C
解析
： C is correct. The probability of an up move （ ） can be found by solving the equation: （ ）uS ＋ (1 – p)dS = （ ）105 ＋ (1 – p)97 = 102. Solving for p gives 8p = 5, so that p = 0.625. C正确。 向上移动（ ）的概率可以通过求解下列方程得到:（ ）uS＋(1 - p)dS = （ ）105＋(1 - p)97 = 102。解p得到8p = 5，所以p = 0.625。 题目中描述1mil次伯努利实验后，可以得到平均价格102美元，这里指的是通过概率计算出来的平均价格。伯努利事件只有两个结果，结合本题，上涨和下跌，我们知道了对应的幅度，可以计算概率p和1-p。