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s价格不确定要short forward contract而不是long forward contract？
