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小王爱学习 · 2022年03月24日

大于小于分红的理解

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021205000031

问题如下：

A stock provides dividends of USD 0.25 per share every three months. The next two ex-dividend dates are in two months and five months. The risk-free rate is 4% per annum. At what times might a six-month American call option with a strike price of USD 50 be exercised?

选项：

解释：

The possible exercise times are immediately before the stock goes ex-dividend at the two-month point and the five-month point, as well as at the end of the option's life. The ex-dividend dates are after 0.16667 and 0.41667 years, and the end of the option's life is after 0.5 years. Because:

0.25 < 50(1 -e−0.04X(0.41667−  0.16667)e^{-0.04X(0.41667-\;0.16667)}]

we can use the results at the end of Section 15.7 to show that the option should never be exercised at the two-month point. Because:

0.25 > 50(1 -e−0.04X(0.5−  0.41667)e^{-0.04X(0.5-\;0.41667)}]

the option will sometimes be exercised immediately before the five-month point. Possible exercise times are therefore at five months and six months.

是不是只要计算出来大于分红，不管put还是call，都可以提前行权

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1 个答案

李坏_品职助教 · 2022年03月24日

嗨，努力学习的PZer你好：


对于支付现金股利（dividend）的股票，美式的call，如果dividend大于行权价 * [1-exp(△T)]，那么提前行权可能是合理的。如果dividend 小于等于行权价 * [1-exp(△T)]，那么就不应该提前行权。


对于美式put，如果股票价格足够低，那么就有可能提前行权，

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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