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摇一摇 · 2023年08月22日

解析没明白,可以再解释一下吗

NO.PZ2023040401000093

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 the fiduciary call expires in the money (meaning that the value of the call, ST – X, is greater than the risk-free bond’s price at expiration, X), then the total value of the fiduciary call is (ST – X) + X, or ST. On the other hand, holding an underlying asset, ST, and buying a put on that asset is known as a protective put. If the put expires out of the money, meaning that the value of the asset, ST, is greater than the put’s value at expiration, 0, then the total value of the protective put is ST – 0, or ST. A protective put and a fiduciary call produce the same result.

解析没明白,可以再解释一下吗

2 个答案

Lucky_品职助教 · 2023年08月23日

嗨,从没放弃的小努力你好:


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),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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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Lucky_品职助教 · 2023年08月23日

嗨,努力学习的PZer你好:


这道题目中涉及到两个组合,

组合一是protective put,组合方式long一份执行价格为X的put option,到期时间为T,再持有一份标的资产,该资产在T时刻的价值为ST,那么根据题目要求,T时刻ST

组合二是fiduciary call,组合方式是long 一份执行价格为X的call option,到期时间为T,再持有一份 面值为X,到期日为T的0息债券,T时刻,call 不行权,组合二的总value为X, 这样两个组合在T时刻的总value是相等的,选择B

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努力的时光都是限量版,加油!