为什么第一个支付股利的时间没有计算？

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:

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

为什么直接计算了3月和六月之间的？

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1 个答案

DD仔_品职助教 · 2024年02月03日

嗨，从没放弃的小努力你好：

这道题计算了两次啊，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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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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eriko · 2024年03月08日

是不是可以这样理解：每个分红的时间点都有可能是行权时间点，在判断3月分红点是否是行权时间时，将下个分红点6月看作为maturity T?

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NO.PZ2020021203000073问题如下A seven-month call option pays vin of US0.5 in three months ansix months. The strike priis US40. Assume a constant risk-free rate of 8% per annum (annually compoun for all maturities. Is it ever optimto exercise the option before maturity? Explain. It is only optimto exercise immeately before a vinpayment. Immeately before the three-month payment, the option holr shoulwait, because there are three months until the next vinpayment anK - K* is greater ththe vinpayment:K−K∗=40−401.080.25=0.76 0.5K-K^\ast=40-\frac{40}{1.08^{0.25}}=0.76 0.5K−K∗=40−1.080.2540=0.76 0.5Exercise coptimimmeately before the six-month vinpayment because there is only one month to maturity anK - K* is less ththe vinpayment:K−K∗=40−401.081/12=0.26 0.5K-K^\ast=40-\frac{40}{1.08^{1/12}}=0.26 0.5K−K∗=40−1.081/1240=0.26 0.5这里说annually compoun，怎么用e折现呢，e不是连续复利嘛？

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