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薛真 · 2020年03月16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

市场价格S0从哪得出？

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1 个答案

小刘_品职助教 · 2020年03月16日

同学你好，

这道题不需要市场价格，用执行价格带入计算。执行价格是40:-)

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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