Your price for the put is unrealistic. If the stock is at $18, and the put has a strike of $19, then the put is worth at least $1, since otherwise one could buy the put and the underlying stock, and immediately exercise the put (assuming it is American, as is usual for stocks), to get a guaranteed profit. This is called "arbitrage". Any such opportunities are quickly taken advantage of, bringing the price of the put up.
In practice the value of an option is at least its intrinsic value, plus a "time value" component.
As JoeTaxpayer suggested, it may be that you were looking at an old quote. The price the option was last traded at may be quite different from the current bid/asks, because many options are not traded often, and the last trade can easily have been a few days ago.