if I have a stop limit order GTC, and the market closes. What happens to that stop limit order the next morning if the opening price is lower that my stop limit price?
You're talking about a 'stop limit price', but a stop limit order has two prices, a 'stop price' and a 'limit price'. If the 'stop price' is reached (during the day, or in the morning while opening, that doesn't matter), the order becomes a normal limit order selling at the 'limit price' or better. That means that if you use the same price for both, it will only be filled if the price of the stock reaches the 'stop limit price' again. It's more typical (perhaps even mandatory) to have a different limit price, as e.g. in this Investopedia example:
Real World Example of a Stop-Limit Order
For example, assume that Apple Inc. (AAPL) is trading at $170.00 and an investor wants to buy the stock once it begins to show some serious upward momentum. The investor has put in a stop-limit order to buy with the stop price at $180.00 and the limit price at $185.00. If the price of AAPL moves above the $180.00 stop price, the order is activated and turns into a limit order. As long as the order can be filled under $185.00, which is the limit price, the trade will be filled. If the stock gaps above $185.00, the order will not be filled.
Stop Order or Stop Limit Order are no longer "exchange native", which means that they are simulated by your broker.
Take one of the broker as an example:
- Sell Simulated Stop-Limit Orders become limit orders when the last traded price is less than or equal to the stop price.
- Buy Simulated Stop-Limit Orders become limit orders when the last traded price is greater than or equal to the stop price.
In the example above, if the "last traded price" is reached, then the broker would submit a normal Limit Order on your behalf, and if the limit price is also already reached, then it becomes "Marketable" Limit Order on the exchange.
During the Opening Auction as explained in https://money.stackexchange.com/a/111727/24920 , the "last traded price" only concludes when such auction is complete, thefore, the example above may not participate in such Opening Auction. Immediately after such auction, the broker will consider that "last traded price" and continue with the simulation.