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苏·Xu · 2025年01月18日

期权

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。

“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;”也就是在T时刻,put option 是要行权的,价值是Max(0,X-ST),所以是X-ST,P+ST = K - ST + ST = K 这个是什么意思?

1 个答案

李坏_品职助教 · 2025年01月18日

嗨,从没放弃的小努力你好:


题目告诉你,在期末的时候,股票价格ST低于期权的行权价格K,问你protective put的价值与fiduciary call相比,谁高谁低?


protective put = long put option + long stock。在期末的时候protective put的价值 = Max(0, K-ST) + ST,由于题目说股价ST小于K,所以protective put的价值 = K-ST + ST = K.


而fiduciary call = long call option + 面值为K的long risk-free bond,在期末的时候fiduciary call的价值 = Max(0, ST-K) + K =0+K= K(注意ST是小于K的)。


可以看出最后都等于K,所以protective put 与fiduciary call 相等,选B。

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