Yes there is that possibility.
When you sold the call option, you granted to the buyer the right to purchase your shares by paying the strike price per share. The option owner may elect to do that (by exercising the call option) at any time prior to expiration. You have no say in the matter. You cannot force the call owner to
exercise, nor can you prevent it.
As soon as the option is exercised, the option owner is considered to have bought the shares. As with a traditional stock purchase, the stock trade settles three days later. As long as the option is exercised (and you are assigned an exercise notice), the stock has been sold.
If this exercise occurs before the stock trades ex-dividend (without the dividend), then the trade settles in time for the person who exercised the option to be declared the stockholder of record when the stock trades ex-dividend, and hence, collects that dividend. You, as the former shareholder do not get that dividend.
The larger the dividend, the greater the possibility of losing the dividend.
Also, the closer ex-dividend date is to expiration, the greater that possibility.
One point must be mentioned. No one will exercise an option that is not in the money. And the option must be sufficiently in the money before it's owner will exercise. Why?
The call owner has a limited liability. If the stock tumbles, the maximum loss is the value of the call option. Once the exercise is complete, the former option owner now owns stock. If the stock tumbles, the loss can be large – much larger than the loss experienced by the option owner. Thus, the call must be far enough in the money that the person who exercises is willing to take the risk of owning stock instead of the call option. The break point comes at the strike price of the option. The exerciser must be willing to bet – and the payoff is the dividend – that the stock will not tumble below the strike price – where the loss can be substantial.
When exercising, the best time is one day before the stock trades ex-dividend.
You learn about being assigned an exercise notice the morning after the option owner exercises. Thus, if you see that you still own the shares on the morning the stock goes ex-dividend, then you collect the dividend. When you no longer own the stock, and are no longer short the call option, on that ex-dividend day, then you do not collect the dividend. How can you determine the likelihood of being assigned for that dividend? If the call option is trading at parity – and that means it has zero time premium – and if the delta is 100, then it's right for the call owner to exercise. Some call owners exercise more aggressively, but that is beyond your control.
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