问题如下:
Using one-period binomial model, Jack calculated that the terminal value of a stock is $55, if the current price is $50, the size of an up move is 1.25 and a down move is 0.8. The probability of a down move that Jack picked is:
选项:
A.0.50
B.0.67
C.0.33
解释:
C is correct. The probability of an up move is p, then the probability of a down move is (1-p). Draw the equation that (p)uS + (1 – p)dS = (p)×50×1.25+ (1 – p)×50×0.8 = 55. Solving the equation, p = 0.67, so (1-p) = 0.33.
从题目中能够得到金额50x1.25=62.5,以及50x0.8=40,以及选择上的机率是P,选择下降的机率是1-p。那么请问为什么可以把机率x金额(Px62.5+(1-p)x40)=第二级的金额(55)的不等式呢?我记得老师在课堂中只讲到,把第一级的机率X第二级的机率,然后把两组机率相加就是最终的probability,但是并没有提到实际乘以金额的方法。