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花儿。 · 2023年05月09日

K不是行权价吗?

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。

为什么这里又说K是risk free bond呢?

p+s=c+k,我理解是put 价格 + spot 价格 = call 价格 + 行权价(固定的常数)

其实是因为这个是固定常数,所有才说risk free,但是为什么bond。

1 个答案

Lucky_品职助教 · 2023年05月11日

嗨,爱思考的PZer你好:


在金融领域,无风险收益通常由国债或其他具有相似信用评级和流动性特征的债券构成。因此,在这道题中,当提到无风险债券时,债券实际上是指具有相似特征的债券,而非特定的一种债券。这里借用“债券”这个词语来描述具有无风险收益特征的产品类型。另外,根据put-call-forward parity的公式 P + long forward contract + long risk-free bond = C + K,我们知道K是未来的现金流,可以看作一个未来的支付承诺,因此这里也称之为无风险债券。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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