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刘美 · 2024年08月05日

这里说annually compounded啊，怎么用e折现呢，e不是连续复利嘛？

  1. FRM I
  2. Financial Markets And Products

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.

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

这里说annually compounded啊，怎么用e折现呢，e不是连续复利嘛？

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pzqa27 · 2024年08月06日

嗨，爱思考的PZer你好：


我看解析并没有用e进行折现，是直接除的1.08.

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刘美 · 2024年08月06日

sorry眼花了😓

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