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椰子鸡 · 2024年05月18日

CK=PS

  1. CFA I
  2. Derivative

NO.PZ2023040401000096

问题如下：

Under put–call–forward parity, which of the following transactions is risk free?

选项：

A.

Short call, long put, long forward contract, long risk-free bond

B.

Long call, short put, long forward contract, short risk-free bond

C.

Long call, long put, short forward contract, short risk-free bond

解释：

A is correct. Purchasing a long forward contract and a risk-free bond creates a synthetic asset. Combining a long synthetic asset, a long put, and a short call is risk free because its payoffs produce a known cash flow of the value of the exercise price.

CK=PS

S-F=rf


C+K=P+F+rf

rf=C+K-P-F


这么推到有什么问题？

和选项对不上啊

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1 个答案

李坏_品职助教 · 2024年05月18日

嗨，爱思考的PZer你好：


这道题让你用put–call–forward parity公式：

把第二行这个公式做变形：

p - c +F(T) / (1+r)^T - X/(1+r)^T = 0，

现在我们把等式左右侧都 + 2 * X/(1+r)^T，

这样的话，p - c +F(T) / (1+r)^T + X/(1+r)^T = 2 * X/(1+r)^T.


注意看这个等式右侧是一个无风险债券，所以我们得到了 risk free的结果。等式左侧是long put , short call, long forward, long risk free bond。对应的就是A选项了。


你写的推导过程里面的C+K/(1+r)^T = P+S, 那是put-call parity，不是本题要求的“put–call–forward parity”。




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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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