问一道题：NO.PZ2019070101000019

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：

Strategy I.

Strategy II.

Strategy III.

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}} = $ 2.47,$ 所以应该现在行权。

未来预期收益怎么算

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品职答疑小助手雍 · 2020年03月24日

同学你好，6个月之后收益为4的概率是63%，37%的概率收益为0，所以可以求出未来预期的收益就是0.63*4。再用rf折6个月就是未来预期收益的现值，肯定是小于5的，所以应该现在行权。

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薛真 · 2020年03月30日

谢谢

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NO.PZ2019070101000019 问题如下 The value of a 6-month Americcall option is either $4.00 maturity with a probability of 0.63 or $0 with a probability of 0.37, exercise priis $40. Current stopriis $45, ancontinuously compounrisk free-rate is 4%. Whiof the following strategy cachieve maximum return:I. exercise the option, because the payoff from exercising the option is more ththe present value of the expectefuture payoff.II. exercise the option, because the option is in-the-money.III. not exercise the option A.Strategy I. B.Strategy II. C.Strategy III. None. 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 : (4×0.63)+(0×0.37) e (0.04)×0.5 =$2.47, 所以应该现在行权。 1.现在行权的gain是5，期权价值低于5，这个我理解，但是美式看涨不是等待有价值么？2.那美式看涨怎么判断要不要行权，是不是一旦出现s-x大于c的现值，就应该行权，不要再等了？

2024-10-20 10:23 1 · 回答

The value of a 6-month Americcall option is either $4.00 maturity with a probability of 0.63 or $0 with a probability of 0.37,这块的VALUE指的是看涨期权的收益还是价值，如果是价值的话是不是可以理解成期权费？

2020-03-23 16:27 1 · 回答

为什么strategy2不对现在S大于X 那就是In the money 现在行权合算啊

2019-11-06 13:26 1 · 回答

啥啥啥不是说美式看涨不应该提前行权。。看跌可以提前行权吗？【建议卖掉不建议行权啥的？

2019-10-19 15:39 1 · 回答

问一道题：NO.PZ2019070101000019

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