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Luhunlu · 2022年03月03日

老师,关于另一种套利方法

NO.PZ2016082402000028

问题如下:

The current price of stock ABC is $42 and the call option with a strike at $44 is trading at $3. Expiration is in one year. The corresponding put is priced at $2. Which of the following trading strategies will result in arbitrage profits? Assume that the risk-free rate is 10% and that the risk-free bond can be shorted costlessly. There are no transaction costs.

选项:

A.

Long position in both the call option and the stock, and short position in the put option and risk-free bond

B.

Long position in both the call option and the put option, and short position in the stock and risk-free bond

C.

Long position in both the call option and the risk-free bond, and short position in the stock and the put option

D.

Long position in both the put option and the risk-free bond, and short position in the stock and the call option

解释:

ANSWER: C

Answers A and B have payoffs that depend on the stock price and therefore cannot create arbitrage profits. Put-call parity says that cp=32=$1c-p=3-2=\$1 should equals SKerτ=4244×0.9048=$2.19S-Ke^{-r\tau}=42-44\times0.9048=\$2.19. The call option is cheap. Therefore buy the call and hedge it by selling the stock, for the upside. The benefit from selling the stock if S goes down is offset by selling a put.

老师,我想确认一下除了C选项的另一种套利方法:


因为目前put option的市场价格高于根据put-call parity算出的合成价格,所以应该long P合成,short P市场,

其中P合成=C+K-S,所以综上,套利策略应该是long call ,long bond,short stock and short put,这样对吗?



1 个答案
已采纳答案

品职答疑小助手雍 · 2022年03月03日

同学你好,对的,long低的合成P,short市场上价高的P。

Luhunlu · 2022年03月03日

好的,感谢老师解答!

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