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苏·Xu · 2025年01月18日

put-call

  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。

  1. CK=PS 中求的是哪一个？
  2. CKPS中，C是call option, P 是put option, K 是bond，S是stock/asset 对吧？NO.PZ2016031201000045 和 NO.PZ2016031201000045 中解析是这么说的


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1 个答案

李坏_品职助教 · 2025年01月18日

嗨，爱思考的PZer你好：


题目问你，哪一个选项是无风险的？意思是问你K如何构造出来（K在讲义里也写作X）。另外此题说的是put–call–forward，所以用到的公式不是简单的C +K = P + S，而是下面这个：

直接看第一行的公式，X/(1+r)^T = F0(T)/(1+r)^T + p - c，这样就把X这个无风险资产构造出来了。A选项的short c, long p, long forward正好符合，再加一个long risk- free bond，那相当于是两份无风险资产。所以A选项符合要求。



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