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小悟空 · 2020年05月29日

问一道题：NO.PZ2018062016000095

  1. CFA I
  2. Quantitative

问题如下：

Using two-period binomial model, Jack wants to calculate the terminal value of a put option. If the current price of the underlying asset is $150 and the strike price is $120, the size of an up move is 1.69 and a down move is 0.59. Only when the price is below the strike price can the option has a positive value, otherwise the value will be zero. How many terminal nodes can give back positive return？

选项：

A.

1

B.

2

C.

0

解释：

A is correct. Only the third node has a value less than $120, which is $52.22.

老师您好，请问one-period binomial 和 two-period binomial是什么意思？ terminal value一般都是指两年后的价钱吗？ 这道题没有说算两年后的值啊？


谢谢老师


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星星_品职助教 · 2020年05月29日

同学你好，

one-period 指的就是一期二叉树，以本题为例，就是150只分叉到253.5和88.5就结束了；同理， two-period就是两期二叉树，就是本题的形式，150后在分叉后又分了一次，最后有了428.42,149.57和52.22三个结果。

（option）terminal value指的是二期二叉树后这个期权应该值多少钱，这个涉及期权估值，比较复杂，并不是本题以及数量里的考点。本题考察的是如果仅考虑最后一期对应的428.42,149.57和52.22三个结果（这个三个结果就是三个terminal nodes），哪个结果能带来positive return。由于put option是跌过了strike price =120才行权，三个结果中只有52.22低于了120，所以能带来正收益的点就只有52.22这一个terminal nodes，到这里这道题就已经做完了。选择一个terminal nodes即A选项即可。

 

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