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jvniki · 2024年03月03日

有点懵 能否用画图大法讲解一下

  1. CFA I
  2. Quantitative

NO.PZ2023052407000012

问题如下：

A stock currently trades at USD25. In one year, it will either increase in value to USD35 or decrease to USD15. An investor sells a call option on the stock, granting the buyer the right, but not the obligation, to buy the stock at USD25 in one year. At the same time, the investor buys 0.5 units of the stock. Which of the following statements about the value of the investor’s portfolio at the end of one year is correct?

选项：

A.

The portfolio has a value of USD7.50 in both scenarios

B.

The portfolio has a value of USD25 in both scenarios

C.

The portfolio has a value of USD17.50 if the stock goes up and USD7.50 if the stock goes down.

解释：

A is correct. Regardless of whether the stock increases or decreases in price, the investor’s portfolio has a value of USD7.50 as follows:

If stock price goes to USD35, value = 0.5×35 – 10 = 7.50.

If stock price goes to USD15, value = 0.5×15 – 0 = 7.50.

If the stock price rises to USD35, the sold call option at USD25 has a value to the buyer of USD10, offsetting the rise in the stock price.

如题 请帮忙用画图大法解答一下

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4 个答案

品职助教_七七 · 2024年05月14日

嗨，从没放弃的小努力你好：


@Lila 提问中引用的句子就是解释call是负号的原因，需要进一步说明一下这句话是哪个地方没理解。只是简单的把这一句换个角度重说一遍没有意义。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

品职助教_七七 · 2024年03月23日

嗨，从没放弃的小努力你好：


@卓娅

本题涉及到的字母：

V：构建的无风险组合的市场价值；

h：hedge ratio，可以简单理解为需购买的股票份数；

S：股票价格

C：call option市场价值。

数字角标为期限，0为当下，1为一期后。


减C的原因是本题背景为sell call。所以call价值升高，购买方行权，seller需要向购买方支付此时Call的市场价值，所以是减号。

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努力的时光都是限量版，加油！

Lila · 2024年05月14日

减C的原因是本题背景为sell call。所以call价值升高，购买方行权，seller需要向购买方支付此时Call的市场价值，所以是减号。 这句话没看懂，请帮忙再解释一下为什么call是-号，谢谢

卓娅 · 2024年03月23日

每个字母代表啥能不能具体解释一下，尤其是公示中一个加一个减，怎么判断怎么解释，谢谢

品职助教_七七 · 2024年03月03日

嗨，努力学习的PZer你好：


本题要计算无风险组合的价值。不需要画图，可根据sell call情况下无风险组合的公式V0=h*s-C0，写出股价上升或下降时的情况：

股价上升时： V1=h*s1-C1。

股价下降时：V1=h*s1-0


题干给出h=0.5，股价上升时的S1=35，股价上升时的C1=35-25=10，所以V1=0.5×35 – 10 = 7.50.

股价下降时的S1=15，所以V1=0.5*15-0=7.50.

由于是无风险组合，所以两种情况下的V1必然一样，算一个就行。选择结果为7.50的A选项即可。

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努力的时光都是限量版，加油！

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