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xiaobaiybz · 2025年04月22日

请老师解释下这道题,谢谢

NO.PZ2023091802000140

问题如下:

An investor holds an American call option on a dividend paying stock with the following characteristics

Current stock price ,S=USD 50

Strike price, K=USD 50

Time to expiration ,T=2 mouths

A divided, D, of USD 1 per share has just been announced ,with an ex-dividend date, t, of one month from now, Assuming the risk-free rate, r, is 1.5% and the option stays at-the-money, is it optimal to exercise the option right before the ex-dividend date?

选项:

A.

Yes, because S < K*exp(-r(T-t)) + D

B.

Yes, because D>K*(1-exp(-r(T-t)))

C.

No, because the call option is at-the-money ,and early exercise is only optimal when it is deep in-the-money

D.

No, because unlike an American put option, it is never optimal to exercise an American call option early.

解释:

请老师解释下这道题,谢谢

1 个答案

李坏_品职助教 · 2025年04月22日

嗨,从没放弃的小努力你好:


题目问你,在除息日之前提前行权的话,是否是最佳选择?


这是个美式看涨期权,参考基础班讲义的讲解:

如果分红1USD 小于 X - PV(X),那就不要提前行权。 但是这道题的X - PV(X) = 50-50/e^(1.5%*1/12) = 0.0625.

很显然分红的1美元 大于0.0625,所以B选项是对的,应该要提前行权。

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