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比如世界 · 2020年02月21日

问一道题：NO.PZ2020021203000073 [ FRM I ]

  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.

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

可以用中文讲一下解题思路吗？这道题目的考点不是很明白。谢谢老师

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orange品职答疑助手 · 2020年02月21日

同学你好，本题题目没说清，它其实应该是一个美式期权。它考察的是，美式期权何时提前行权会划算，对应的考点是下面这个，建议同学复习下这个知识点或者重听一下原理：

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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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