I understand that it is possible for a European put option to trade below its intrinsic value (i.e. assuming a positive risk-free rate, the theoretical lower bound of a European put is lower than its intrinsic value). In such cases, the European put option has negative time value. My question is: do European puts sell below intrinsic value in real life? Or is the theoretical lower bound only theoretical?
Note: I have no real-world experience in trading derivatives. My knowledge of derivatives is completely theoretical, hence this question.