TZXคิดถึง · 2020年03月07日

问一道题：NO.PZ2018062007000085

问题如下：

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

选项：

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

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

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.

能解释一下这道题么？没看懂

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4 个答案

已采纳答案

xiaowan_品职助教 · 2020年03月07日

嗨，努力学习的PZer你好：

同学你好，这道题考察的是put-call parity的一个变型。

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，

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。

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