ANY option I BUY shows up in my platform with a negative theta. It's not exactly rare. I seem to recall a short, European-settled option might show a positive theta, but I've never seen it and may be way off.

"Negative time value is rare". I got that from the book "New Insights On Covered Call Writing" by McMillan and another guy. Is that a typo?

theta is always negative. If you short options or spreads, then the negative theta helps you but theta is always expressed as a negative number. Anal Option Police

Time value is not the same as theta. Theta is the change in time value per day. That being said, it is possible to have positive theta on a bought option and negative theta on a sold option. Two possible causes are a corporate action or a dividend. Even then, time value only appears negative, when in fact your pricing of the option was wrong.

How do you get "negative TV" as stated in the book even though McMillan says it's rare, assuming there's no miscalculation?

Theta is the dollar value change per day. Time value is the part of the option premium that is NOT intrinsic value. Time value of option is the not same as theta. Theta is always negative for option buyers. Theta is always positive for option sellers. It is not possible any other way.

I can't think of a situation that someone would PAY YOU to allow them to take on risk. Negative Time Value would require the option to be worth less than its intrinsic value. Who would sell you that? Perhaps he meant combinations of options?