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水瓶公主 · 2023年03月02日

只能在分红日判断行权吗

  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?

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.

这道题假定的是只能在分红日行权吗？为什么不是1/2—1/6

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品职答疑小助手雍 · 2023年03月02日

同学你好，肯定是在分红日前行权的，因为分红后再行权的话S就会直接下降，减X的收益就少了。

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。

然后拿0.25作比较的肯定就是两个付息日之间的时间差了，也就是用（5/12减去2/12）作为T折现。

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