A stock priced at $ 20 has an 80 percent probability of moving up and a 20 percent probability of moving down. If it moves up, it increases by a factor of 1.05. If it moves down, it decreases by a factor of 1/1.05. What is the expected stock price after two successive periods（）
A. $ 20.05.
B. $ 22.05.
C. $ 21.24.
参考答案：C
解析：
If the stock moves up twice, it will be worth $ 20×1.05×1.05=$ 22.05. The probability of this occurring is 0.80×0.80=0.64. If the stock moves down twice, it will be worth $20×(1/ 1.05)×(1/1.05)=$18.14. The probability of this occurring is 0.20×0.20=0.04. If the stock moves up once and down once, it will be worth $ 20×1.05×(1/1.05)=$ 20.00. This can occur if either the stock goes up then down or down then up. The probability of this occurring is 0.80×0.20+0.20×0.80=0.32. Multiplying the potential stock prices by the probability of them occurring provides the expected stock price: $ 22.05×0.64+$ 18.14×0.04+$20.00×0.32=$21.24.