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
题目中没有任何信息说非要考第二个公式吧