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Infinite · 2020年03月03日

问一道题：NO.PZ2020021203000073

  1. FRM I
  2. Financial Markets And Products

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∗=40−401.080.25=0.76>0.5K-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∗=40−401.081/12=0.26<0.5K-K^\ast=40-\frac{40}{1.08^{1/12}}=0.26<0.5

"在三个月的时候不行权的话用执行价格折现应该是4/12个月份呀为什么答案用的3/12" 看到有位同学问的这个问题，他应该问的是公式里是x-xe^(rf(T-t), 7个月的option, 在三个月的时候行权，大T-小t ,不应该是（7-3）/12=1/3吗？

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3 个答案

orange品职答疑助手 · 2020年03月05日

@安安鱼

李老师上课讲的板书如下图所示。对应本题里，应该是站在t=6月这个节点上去判断。但如果判断的时点和到期日之间，还存在着分红时间点的话，那应该代入这个时间点到下个分红时间点的T，而不是这个时点到期权行权日的T。

安安鱼 · 2020年03月04日

还是不懂为什么是3/12按照李老师讲的应该是4/12

orange品职答疑助手 · 2020年03月03日

同学你好，这边应该是三个月的间隔，应该是这一次支付股利的时刻，到下一次支付股利的时刻，中间的时间。

如果这一期之后期权会到期，那么折现时间应该是T-ti 。否则就是 ti+1 - ti

你可以看一下郑振龙这里的书（10.13式），这个结论是没错的，但它推导的过程比较难。我觉得这个小点记忆一下性价比比较高。

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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？

2024-08-05 20:09 1 · 回答

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 为什么直接计算了3月和六月之间的？

2024-02-01 18:35 1 · 回答

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请问这是基础课程哪一块的知识点

2023-03-09 09:04 2 · 回答

NO.PZ2020021203000073 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

2021-10-17 17:31 1 · 回答

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