问一道题：NO.PZ2019052801000059

问题如下：

The current price of a stock is $100, the risk-free rate is 4%, an American call and put option on the stock has an expiration of 9 months and a strike price of 95. the lower bound and upper bound of the difference of the value of the American call and put option on this stock are close to?

选项：

$5, $6.53.

$5, $7.81.

$5, $7.21

$7, $7.81.

解释：

B is correct.

考点：Put-Call Parity.

美式看涨看跌期权的价格区间为： $S_0-X\leq C-P\leq S_0-Xe^{-rT}$

100- 95=5 ≤ C − P ≤ 100 − 95 $e^{-0.04\;\times0.75}$=7.81

$\$5\leq C-P\leq\$7.81$