Based on the way you worded that, it makes me think you have confused puts and calls. The put allows the person you sold that to to sell the stock to you for $16/share. If the price were trading at say $20/share, the put option would be out of the money and the person holding the option would be better off just selling the shares than to exercise the option. You said "even if the trading price remained below $16" -- when the trading price remains below $16 is the only time exercising the put really makes sense. It is in the money when the spot price is below the strike.