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Yvonne0719 · 2024年09月25日

请问老师这道题是用哪个公式来套的呢？没有特别搞清楚

  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.

请问老师这道题是用哪个公式来套的呢？没有特别搞清楚

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1 个答案

李坏_品职助教 · 2024年09月26日

嗨，从没放弃的小努力你好：


本题问的是根据“ put–call–forward parity”，这个指的是在0时刻的时候，Synthetic protective put = Fiduciary call。

也就是面值为F0(T)的bond + forward + put option = call option + 面值为X的bond。


题目说，如果put option不值钱了，那意思就是在到期日的ST≥X，问你此时的protective put的payoff是多少？

此时，protective put最终的payoff = ST。


这个是因为，protective put = long bond + forward + put，在到期日的时候，long bond的payoff = bond的本金F0(T)，而forward的payoff是ST - F0（T），而put本身是0收益，所以加起来就是ST了，选A。


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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