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🌅 🌅多吉旺珍🌞🌞 · 2020年07月28日

问一道题：NO.PZ2018062016000095 [ CFA I ]

  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.

1，怎么判断该题目需要使用二叉树 2，问题部分理解出现偏出-是要求低于执行价格的情况对吗
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1 个答案

星星_品职助教 · 2020年07月28日

同学你好，

本题就是很典型的应用二叉树的问题，题干中的提示词分别有“two-period binomial model”（直接提示使用二期二叉树模型），和“the size of an up move is 1.69 and a down move is 0.59”（提示需要“分叉”，和分叉后的端点值是多少）。

二叉树更典型的题目是题干中给出current value，然后说下一期这个value有两种变化可能，要么变大，要么变小。然后给出变大/变小的概率，去求下一期的平均值；也有可能给的直接是下一期的均值，然后要求反推概率。

第二个问题的理解涉及到put option，这是一个衍生品的概念，可以先简单理解为当股票价格低于了strike price后，put option就可以行权获利。也就是题干中描述的“Only when the price is below the strike price can the option has a positive value”。题干只要求考虑最终terminal value的情况，所以参考答案解析中的图像，只看最后一期的三个值，只有最下方的一个值$52.22低于了strike price$120。所以选择只有一个点（node）可以提供positive return即可。

在一级考试里，二叉树在衍生品科目里的考察更多一些。

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