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Olivia.W🌸 · 2024年04月21日

call in the money为啥收益不是ST-X？

  1. CFA I
  2. Derivative

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.

call in the money为啥收益不是ST-X？

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1 个答案

李坏_品职助教 · 2024年04月22日

嗨，努力学习的PZer你好：



本题说的是“protective put with forward contract”这个组合，在到期的时候，组合中的put option是out of the money。问你最终的payoff是什么？


protective put with forward contract组合 = long bond(bond的面值等于forward的交割价格F0(T)) + long forward + long put option。

现在题目说put在到期日是价外期权，说明put没有价值，那么这个组合最终的Payoff = long bond的payoff + long forward的payoff = F0(T) + ST - F0(T) = ST。

所以最后的payoff就是基础资产的价格，选A。


这道题和call option没有关系，因为题目说put最后是价外期权，所以在到期日put是没有价值的，只需要考虑forward和bond就行了。

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