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𝒜𝒩𝒥𝒜 安雅🎃 · 2022年01月22日

中文解析为什么说执行价格是K?

NO.PZ2018062007000082

问题如下:

If an underlying asset’s price is less than a related option’s strike price at expiration, a protective put position on that asset versus a fiduciary call position has a value that is:

选项:

A.

lower.

B.

the same.

C.

higher.

解释:

B is correct. On the one hand, buying a call option on an asset and a risk- free bond with the same maturity is known as a fiduciary call. If an underlying asset’s price is less than a related option’s strike price at expiration,the total value of the fiduciary call is X. On the other hand, holding an underlying asset, ST, and buying a put on that asset is known as a protective put. the total value of the protective put is(X-ST)+ST = X . A protective put and a fiduciary call produce the same result.

中文解析:

在T时刻,标的资产价格ST<执行价格K,在此时call option是没有价值的,为0.(因为T时刻是到期日,call的时间价值为0,而ST

所以此时C+K = 0+K=K;

另外一方面,在T时刻,put option的价值=K-ST(因为此时put的时间价值也为0,intrinsic value=K-ST),所以此时P+ST = K - ST + ST = K;

所以C+K = P + S仍然成立。


【问题1】

C+K=P+S

  • C=0,等式左边只剩K
  • P=X-ST,等式右边只剩X

K为什么等于X?


【问题2】

执行价格不是用X来表示吗?K是用来表示bond的吧?

2 个答案
已采纳答案

Lucky_品职助教 · 2022年01月26日

嗨,努力学习的PZer你好:


同学你好~

你的三个问题都是正确的。X是put option的执行价,标的物是股票。

 

本题考查对Put call parity的理解,公式中K是指risk-free zero-coupon bond with a face value of X that matures at T(原版书原话),本题中到了T时刻,protective put中put行权,以执行价X卖掉了手里的股票,收到X元,fiduciary call中call不行权,价值为0,但手里的债券到期,正好面值是X,也收到X元。因此两者是相等的。

 

下面是原版书截图,左侧解释了call expire , put exercise的情况,可以看出total是一样的。

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努力的时光都是限量版,加油!

lynn_品职助教 · 2022年01月23日

嗨,从没放弃的小努力你好:


同学两题其实是一个回答,K的确表示Bond,但是这里K表示的bond的price = 执行价X

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努力的时光都是限量版,加油!

𝒜𝒩𝒥𝒜 安雅🎃 · 2022年01月23日

执行价X是什么东西的执行价?是put option的执行价?那put option又是什么资产的put option,是stock的put option?如果前面三个问题我都说对了,那债券price为何等于stock put option的执行价?

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