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瓦力 · 2025年02月11日

还是不明白为什么期权金是10,以及为什么答案是7.5

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.

期初投资者的portfolio价值是12.5(0.5份股票)+sell call的期权金。一年后,若价格上涨为USD35,会被行权,投资者需要用17.5的价格再买0.5份股票并以12.5的价格卖出,则其portfolio价值是期权金-5;若价格下跌为USD15,不会被行权,但投资者本身持有的0.5份股票价格也跌到了7.5,则portfolio价值还是期权金-5。只能得到两种情况下价值是相等的。

但期权金具体多少本身是买卖双方达成的合约,题目未告知的情况下怎么确定是10?若按照题目答案解析,期权金是10,那按照我上面的思路,最后的答案就应该是5,我的思路是哪里有问题吗?

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