Hi, Suppose a company is trading at $12, then I sell to open a $16 put. Does this mean the buyer can exercise his right to have me buy his stock at $16 before expiration, even if the trading price remained below $16 strike price?
Yes... why would you want to sell a far ITM put anyway? Depending on time to maturity and implied volatility, that put doesn't have a lot of time value. Just a delta long play... with no real upside when the stock really goes through the roof. You can lose $12 down, but can only make $4 up.... (assuming no time value and the price of the put is intrinsic only). You should better buy the 8 call. That way you can only lose $4 down (intrinsic value) and make unlimited upwards.... Or buy the stock and 8 put... same payoff...
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.
OP said it awkwardly, but correctly. Put buyer is forcing OP to buy the stock at 16 (ie put buyer selling the stock at 16).