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Nicole Xiang · 2024年08月16日

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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.

题目解析里的10是什么,怎么理解和怎么计算呢?

2 个答案
已采纳答案

品职助教_七七 · 2024年08月17日

嗨,努力学习的PZer你好:


股价从25涨到35,持有call的一方(buyer)可以以25的价格买入此时已经35的股票,buyer赚10元。

本题为seller的角度,所以就是亏10元,计算中显示为减10,即解析中的:

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


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

花儿。 · 2024年09月09日

这道题中,t=0时刻已经购入了0.5单位的stock。这个value其实是除去0时刻投资,要算的是在t时刻这个portfolio还需要付多少钱或者赚多少钱是吗?

品职助教_七七 · 2024年09月10日

嗨,努力学习的PZer你好:


@花儿。 value指的是市场上现在期权和股票的价值,不考虑“0时刻投资”。

接着原回复,此时股票的市场价值是35。call的市场价值是10,但站在seller的角度就是-10。所以组合才显示如下:

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

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努力的时光都是限量版,加油!

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