怎么判断美式看涨是否行权

问题如下：

The value of a 6-month American call option is either $4.00 at maturity with a probability of 0.63 or $0 with a probability of 0.37, exercise price is $40. Current stock price is $45, and continuously compounded risk free-rate is 4%. Which of the following strategy can achieve maximum return:

I.   exercise the option, because the payoff from exercising the option is more than the present value of the expected future payoff.

II.  exercise the option, because the option is in-the-money.

III. not exercise the option

选项：

A.

Strategy I.

B.

Strategy II.

C.

Strategy III.

D.

None.

解释：

A  is correct.

考点：Other Issues

解析：对于美式看涨期权，现在行权可以获得$45-$40=$5,

如果现在不行权，未来预期收益的折现值为  : $\frac{(4\times 0.63)+(0\times 0.37)}{e^{(0.04)\times 0.5}}=\$\mathrm{2.47, }$所以应该现在行权。