Why Do OTM Options Still Have a Small Amount of Time Value?
Out-of-the-money (OTM) options still have a small amount of time value because there is a non-zero probability that the underlying asset's price will move enough before expiration to make the option in-the-money. This possibility of future profit is the time value.
The longer the time to expiration and the higher the volatility, the greater this time value will be.