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bunnymiss · 2020年02月24日

问一道题:NO.PZ2020021203000073 [ FRM I ]

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.

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:

KK=40401.080.25=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:

KK=40401.081/12=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
1 个答案

品职答疑小助手雍 · 2020年02月24日

同学你好,三个月的折现不就是3(个月)/12(个月)么

bunnymiss · 2020年02月24日

不是啊 还剩四个月

品职答疑小助手雍 · 2020年02月25日

哦哦,我明白你意思了,那个股利日确实是还有4个月,我跟后台反馈下,谢谢指出。

品职答疑小助手雍 · 2020年02月25日

额。。。不对,我刚又看了下,要折现的是到下一次股利支付日的时间,也就是3个月,不是4个月。所以还是应该折3个月的。

bunnymiss · 2020年02月25日

为什么折现到下次股利支付日呢

品职答疑小助手雍 · 2020年02月25日

因为当前是否行权和下次分配股利没关系啊。

bunnymiss · 2020年02月27日

为什么不是折现到到期日

品职答疑小助手雍 · 2020年02月27日

往到期日折的话不就和下次分配股利有关系了么

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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

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