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Gloria_趙(林青) · 2022年07月01日

老师,可否讲解一下公式long asset+short forward=long risk free

NO.PZ2018062007000051

问题如下:

Which of the following statements best describes put-call-forward parity?

选项:

A.

A fiduciary call is equivalent to a protective put with a forward contract.

B.

A fiduciary call is equivalent to a protective put.

C.

A fiduciary call is equivalent to the combination of short put plus long risk-free bond and long a forward contract.

解释:

A is correct.

According to put-call-forward partiy, a fiduciary call is equivalent to a protective put with a forward contract.

中文解析:

C+K=P+S,fiduciary call=protective put

long asset+short forward=long risk free bond (购买有风险的资产同时short forward可以转移风险,获得无风险收益)

那么long asset=long risk free bond +long forward, risk free bond的面值为FP,将
long asset=long bond+long forward

代入 protective put,即P+S=long put+long bond( 面值为FP)+long forward,等式右边也称为protective put with forward

我们可以发现无论期末股票价格如何变化, fiduciary call与protective put with forward的结果是相同的。

既然期末的outcome是相同的,所以期初构建两个portfolio的成本也应该相同。

fiduciary call的成本=C0+K/(1+rf)^T,而

protective put with forward的成本为P0+FP/(1+rf)^T( long forward期初不支付现金,所以没有成本)

这样就能得到put call parity with forward的公式了,即

C0+K/(1+rf)^T=P0+FP/(1+rf)^T

看老师的讲解里面long asset+short forward=long risk free这个公式,不知道可否详细讲解一下。short forward有点不是很理解。谢谢!

1 个答案

Lucky_品职助教 · 2022年07月02日

嗨,从没放弃的小努力你好:


我们可以从收益图形来理解,横轴是股价,纵轴是收益,long asset就是一条斜率为正的直线,short forward是一条斜率为负的直线,两者结合,就是一条水平线,即risk free收益,无论股价怎么变化,收益都是固定的。

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