NO.PZ2016031201000051
问题如下:
Combining a protective put with a forward contract generates equivalent outcomes at expiration to those of a:
选项:
A.fiduciary call.
B.long call combined with a short asset.
C.forward contract combined with a risk-free bond.
解释:
A is correct.
Put−call forward parity demonstrates that the outcome of a protective put with a forward contract (long put, long risk-free bond, long forward contract) equals the outcome of a fiduciary call (long call, long risk-free bond). The outcome of a protective put with a forward contract is also equal to the outcome of a protective put with asset (long put, long asset).
中文解析:
本题考察的是put-call-forward parity,它的推导逻辑如下:
因为 long stock+short forward 可以合成一个无风险头寸,即Long risk-free bond(注意这里的bond面值为远期合约价格,即FP)
将该等式变形可得: long stock=long forward+long risk-free bond,
所以proctive put with asset= long put+long stock中的stock可以用上面粗体的公式替代,可得:
protective put with forward= long put+long forward +long risk-free bond
我们发现无论期末股票价格如何变化,protective put with forward的payoff与fiduciary call是一样的。具体过程如下图:
这里再强调一遍,protective put with forward中的bond面值为FP,而fiduciary call中的bond面值为X。
put call forward parity不应该是C+K=P+FORWARD+BOND吗,题干只说了forward和put,不应该还少了一个bond吗