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AgnesWu · 2023年05月19日

关于risk free的理解

  1. CFA I
  2. Derivative

NO.PZ2018062007000085

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.

中文解析：

这道题考察的是put-call parity的一个变形。

我们知道S是一个不确定的现货价格，那么假设持有S同时short forward contract，就可以得到一个无风险收益，可以等效为一个risk-free bond，也就是S + short forward contract = long risk-free bond，等式两边变换一下可以得到：S = -short forward contract + long risk-free bond = long forward contract + long risk-free bond；

再把这个等式带入到P + S = C + K，得到P + long forward contract + long risk-free bond = C + K，K是无风险债券 Risk free bond，

K = P + long forward contract + long risk-free bond - C，这样就构造了一个无风险组合，A选项对。

题面问的risk free，我首先反应为公式c+K=p+F+rf 所以变形以后三个答案都不匹配。我想问的是若不从答案出发反推问题，这个问法是不是也可以理解为forward折现的rf

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Lucky_品职助教 · 2023年05月20日

嗨，爱思考的PZer你好：


你的思路也可以，K是无风险债券，K = P + long forward contract + long risk-free bond - C，这样就构造了一个无风险组合，也就是A选项。

put–call–forward parity中两个risk free bond的面值不同~

protective put with forward contract 中risk free bond面值是forward price，会有债券本身需要面临的风险。而题干问的是无风险，意味着这些组合应当能获得无风险收益的情况。所以计算的是k

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CFA一定过！ · 2023年12月09日

我也是和提问题的人一样的思路，也是想到那个公式。 但还是不理解为什么不是求Rf

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