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Cooljas · 2024年04月29日

这个题可以再详细解释下吗?

NO.PZ2023091802000103

问题如下:

An investor sells a January 2019 call on the stock of XYZ Limited with a strike price of USD 50 for USD 10, and buys a January 2019 call on the same underlying stock with a strike price of USD 60 for USD 2. What is the name of this strategy, and what is the maximum profit and loss the investor could incur at expiration?

选项:

A.

Strategy: Bear spread Max Profit: USD 8 Max Loss: USD 2

B.

Strategy: Bear spread Max Profit: Unlimited Max Loss: USD 2

C.

Strategy: Bull spread Max Profit: USD 8 Max Loss: USD 2

D.

Strategy: Bull spread Max Profit: USD 8 Max Loss: Unlimited

解释:

This strategy of buying a call option at a higher strike price and selling a call option on the same security with the same maturity at a lower strike price is known as a bear spread. To establish a bull spread, one would buy a call option at a lower price and sell a call option on the same security with the same maturity at a higher strike price.

The cost of the bear spread strategy will be:

USD -10 + USD 2 = USD -8 (a negative cost, which represents an inflow of USD 8 to the investor)

The maximum payoff occurs when the stock price ST ≤ USD 50 and is equal to USD 8 (the cash inflow from establishing the position) as none of the options will be exercised. The maximum loss occurs when the stock price ST ≥ USD 60 at expiration, as both options will be exercised. The investor would then be forced to sell XYZ shares at USD 50 to meet the obligations on the call option sold, but could exercise the second call to buy the shares back at USD 60 for a loss of USD -10. However, since the investor received an inflow of USD 8 by establishing the strategy, the total profit would be USD 8 - USD 10 = USD -2.

When the stock price is USD 50 < ST ≤ USD 60, only the call option sold by the investor would be exercised, hence the payoff will be 50 - ST. Since the inflow from establishing the original strategy was USD 8, the net profit will be 58 - ST, which would always be higher than USD -2.

这个题可以再详细解释下吗?

1 个答案

李坏_品职助教 · 2024年04月30日

嗨,从没放弃的小努力你好:


题目问你,这个期权组合叫什么名称?最大的盈利和亏损是多少?


这个人先在较低的行权价K1卖出一份看涨期权,又在较高的行权价K2买入一份看涨期权,这个是典型的bear spread。


bear spread最大盈利是股价下跌到K1以下,比如股价跌到0。那么第一份期权对手不会行权,我们可以白赚期权费10USD。第二份期权我们不会行权,我们损失期权费2USD,所以最大盈利是8USD。


而最大亏损则是当股价涨到K2以上,那么第一份期权对手会行权,我们的盈亏=K1 - 股价 + 10USD,第二份期权我们会行权,我们的盈亏=股价-K2 - 2USD,这俩加起来 = K1-K2 + 8 = -2USD.


所以最大盈利8USD,最大亏损2USD。



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