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emma爱地球 · 2025年01月26日

解题思路

NO.PZ2023040401000099

问题如下:

According to put–call–forward parity, if the put in a protective put with forward contract expires out of the money, the payoff is most likely equal to:

选项:

A.

the market value of the underlying asset.

B.

zero.

C.

the face value of a risk-free bond.

解释:

A protective put with forward contract is defined as a long position in (1) a bond that has the face value equal to the forward contract, (2) a forward contract, and (3) a long position in a put. If the put expires out of the money, the value of the overall position is equal to the market value of the asset.

+ F0(t) (payoff of bond)

+ ST – F0(t) (payoff of forward)

+ 0 (payoff of option)

= ST (payoff of strategy)

B is incorrect. Zero is the payoff of the put alone. This ignores the other positions in the strategy.

C is incorrect. The face value of the risk-free bond is the payoff of the protective put with forward contract if the put expires in the money.

请问中间标黄那一步是不是多余了?用第一个公式,p为0,就剩下s呀,为什么要中间那一步?


1 个答案

李坏_品职助教 · 2025年01月26日

嗨,从没放弃的小努力你好:


本题要求的是用put–call–forward parity(这个意思是要把原始的put call parity里面的现货S替换为forward contract和rf)。


老师第一个公式:这个叫put call parity。

既然题目要求用forward,那么我们需要把现货S替换为forward contract(就是F) + rf,所以C+K = P + F + rf。


现在已知p为0,那么C+K = F + rf = S。


这样是严格按照题目要求来解题,当然,如果直接用C+K = P +S,令P为0也可以得出答案,但是过程不太严谨。



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