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🌅 🌅多吉旺珍🌞🌞 · 2020年07月28日

问一道题:NO.PZ2018062016000095 [ CFA I ]

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
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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