ITM Stocks Going Ex Div

I've got an ITM stock going Ex Div.

I'm not sure how to ask this question.
I do know that there's no free lunch.

If a stock is ITM and going Ex Div, does it make a difference how far out the option is?
Is a stock more likely to be called away if the option is closer in than farther out?

Let's say it's ITM by a buck, and the dividend is 25 cents.

Does it matter if the option is next week or 6 months out for it to be called away?
 
The farther out the expiration date, the higher the Put value.

So if a Call is expiring this Friday, this Friday's same strike Put will be much less value than the same strike Put 6 months out.

So the farther out the expiration, the less likely assignment is because the value is higher farther out?
 
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