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Nicole Xiang · 2023年10月31日

请问B为什么错了

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 synthetic protective put.

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 synthetic protective put 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

synthetic protective put 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

请问B怎么错了呢,没搞懂

1 个答案

pzqa35 · 2023年10月31日

嗨,爱思考的PZer你好:


题目中问的是put-call-forward parity,那么公式如下:


即把put-call-parity中的S换成F0(T)/(1+rf)T那么fiduciary call=long put+long bond+long forward,这是由于在现货市场上可能不能直接买到S,所以采用这种方式来replicate,所以A项是正确的。B项是在put-call-parity中fiduciary call=protective put

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