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菡萏琼琚 · 2022年05月27日

能详细讲一下这个题目吗

  1. CFA I
  2. Quantitative

NO.PZ2017092702000095

问题如下：

A call option on a stock index is valued using a three-step binomial tree with an up move that equals 1.05 and a down move that equals 0.95. The current level of the index is $190, and the option exercise price is $200. If the option value is positive when the stock price exceeds the exercise price at expiration and $0 otherwise, the number of terminal nodes with a positive payoff is:

选项：

A.

one.

B.

two.

C.

three.

解释：

A is correct.

Only the top node value of $219.9488 exceeds $200

为什么要分裂到第三次，另外选择A，这个one代表的是什么？

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星星_品职助教 · 2022年05月27日

同学你好，

题干提示了“ using a three-step binomial tree”，所以要“分裂三次”，

题目问的是“ the number of terminal nodes with a positive payoff ”，即可以赚钱的节点（node）数量是多少。由于call option可以以200的价格行权（即购买），所以当节点数字超过200时，以200的价格买入就可以赚钱（positive payoff）。这部分实际是衍生品要学的内容，这里可以先简单了解一下。

最后一期一共有四个节点，只有最上面的一个超过了200，所以可以赚钱的节点数量就是one。

菡萏琼琚 · 2022年05月29日

星星老师的讲解每次都很清晰

星星_品职助教 · 2022年05月30日

@菡萏琼琚

感谢支持~学习加油~

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