看了之前的提问还是没有明白第一次股利计算折现时为什么用的是三个月而不是四个月

NO.PZ2020021203000073

问题如下：

A seven-month call option pays dividends of USD 0.5 in three months and six months. The strike price is USD 40. Assume a constant risk-free rate of 8% per annum (annually compounded) for all maturities. Is it ever optimal to exercise the option before maturity? Explain.

选项：

解释：

It is only optimal to exercise immediately before a dividend payment. Immediately before the three-month payment, the option holder should wait, because there are three months until the next dividend payment and K - K* is greater than the dividend payment:

$K-K^\ast=40-\frac{40}{1.08^{0.25}}=0.76>0.5$

Exercise can be optimal immediately before the six-month dividend payment because there is only one month to maturity and K - K* is less than the dividend payment:

$K-K^\ast=40-\frac{40}{1.08^{1/12}}=0.26<0.5$

看了之前的提问还是没有明白第一次股利计算折现时为什么用的是三个月而不是四个月

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DD仔_品职助教 · 2021年10月17日

嗨，爱思考的PZer你好：

同学你好~

美式期权最优的行权时间是分完红之后立刻行权，第一次行权的时间就是3个月的时候，到下一次行权是6个月的时候，这中间差的是3个月，折的时间我们看的是分红之间的时间差，不是到期日，因为到期日他不是最优的行权时间。

第二次行权的时间是第二笔分红之后，那么还没等到下一次（也就是9个月）分红，option就给到期了（7个月），所以6个月到7个月是折1个月。

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看了之前的提问还是没有明白第一次股利计算折现时为什么用的是三个月而不是四个月

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