I sell a put with an expiration of 18 months from now. It is 18 months later and the put is well out of the money. I can let it expire worthless or I can buy the short Put back for one penny. My brokerage company claims that either action will still result in a short term (ordinary income) gain. I have read several articles (including in this forum) that it is a long term gain. The great many trades at a penny a day or two before expiration seems to indicate that by doing so it becomes a long term gain.

What is the answer?