Can an Option’s Time Value Ever Be Negative?

No, an option's time value cannot be negative under normal market conditions. The time value is the portion of the option's premium that exceeds its intrinsic value.

Since the option's premium will, at a minimum, be equal to its intrinsic value, the time value will be zero or positive. A theoretical negative time value would imply that the option is trading for less than its immediate exercise value, creating an arbitrage opportunity that would be quickly exploited by traders, driving the price back up.