When Might Early Exercise of an American Put Option Be Rational?

Early exercise of an American put option may be rational when the option is deep in-the-money and the interest earned on the proceeds from selling the underlying asset (at the strike price) outweighs the option's remaining time value. Specifically, if the underlying asset's price is very low and the strike price is high, exercising early allows the holder to receive the cash immediately and earn interest on it, which can be more valuable than waiting for expiration.