under the assumption that it's very simple.

并从中推导出期权价格
There's only one period between now and exercise;

假设从现在到行权日这一时段是固定的
it's a European option.

这是一份欧式期权
We're going to exercise it in one-- we have an exercise date of one period

我们将在一个确定的未来日期行权
and also under the restrictive assumption--

并且在这种假设条件下
and this is for pedagogical purposes just to simplify option theory--

这是出于教学目的对期权理论进行的简化
that the stock price, S, is the stock price today.

S是股票的现价
The stock--this stock is very special

该支股票非常特别
because next period it can have only two values.

即在到期日股价只有两种变化可能
It's S times u if the stock goes up;

如果上涨则股价变为S乘以u
u stands for up.

u代表上涨 [u=1+涨幅]
It's S times d if the stock price goes down.

如果下跌则股价变为S乘以d [d=1+跌幅]