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tristabo · 2024年05月30日

为什么是short stock

NO.PZ2020021203000077

问题如下:

A European call and European put option on a stock both cost USD 5 with a common strike price USD 30 and a common time to maturity of one year. The current stock price is USD 30. What arbitrage opportunities does this create? Assume no dividend is paid and the interest rate is positive.

解释:

From put-call parity, the excess of the call price over the put price is S - PV(K). In this case S = K = 30 and so S - PV(K) is positive. The call should be worth more than the put, but they are both worth the same. An arbitrageur should buy the call, sell the put, and short the stock.

Call市场价格低谷,所以long call short put,那么根据put call parity公式,怎么推断出short stock

1 个答案

李坏_品职助教 · 2024年05月30日

嗨,爱思考的PZer你好:


put-call parity的公式:


把上面等式变形:c-p= S - X*e-rt

正常情况下,当S=X时,S - X*e-rt>0,相同行权价的call价格应该高于pu。


但是现在的条件是c=p了,这说明上面划线的等式左侧是等于0了,但等式右侧依然是大于0,出现了矛盾(等式左侧被低估)。所以我们要买入等式左侧的组合(也就是long call and short put),并卖出等式右侧的组合(也就是卖出S,然后把现金按照利率r进行储蓄)。所以是short stock。


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