Given my limit order and the ask price, what do I really pay for my stock?

Question

I anticipated there would be many answers to this already, but couldn't find any. I am aware of this question: How is stock price determined?, and I think I can deduce the answer from it, but I am very unsure, so I prefer a direct answer.

Let me best give an example. Recently, I noticed a sharp decline in the (last) price of the stock S. I placed a limit order for 10 stocks with a limit EUR 51,74. I got them on the next day at the opening for exactly EUR 51,50.

So, my question is: How does the price at which I buy really come about. Is it the cheapest selling price (ask) compliant with me order (meaning sellers always loose), is it the mean between my limit and the ask? Is it something entirely different?

Conversely, if I sell the stock with a limit order at EUR 55,00, does it mean I will only get 55,00, although there are people bidding EUR 56,00?

If it depends on the location, answers for XETRA are most appreciated.

EDIT

I think, that the suggested duplicate covers me, but I would like to be certain I understand correctly.

1)I got the stock for EUR 51,50, merely because the sellers ask predated my bid.

2)If the sellers ask of, say. EUR 51,50 had come after my bid, he would have gotten the full 51,74.

EDIT

I try to provide any information desired. Because I saw the comments, I add the following. I apologize, should it be irrelevant. I am (obviously) a newbie.

I ordered on one day shortly after 17:30 using XETRA. I chose the validity option "today" and the option "continuous trade". I was not aware of the stop of trading after 17:30.

The system (German) said that my order was received and would be presented ("vorgetragen") on the next day. Then, on the next day in the morning I got the stock for EUR51,50.

Answer 1

During Continuous trading

When you place an order to Buy at a price lower than the current ask, your order goes to sit in the limit order book, amongst the bids. In this case the bid was 51,74 at the time when your order arrived.

For your order to execute, all the other bids that were in front, at higher prices or the older orders at your price; were either executed against incoming sell orders or cancelled.

So the sellers sent orders against all pending bids at 51.74 51.73 ... 51.52, 51.51... and agains the bids at 51.50 that were older than yours.

Once your bid got to the top of the queue, being the oldest bid at the 51,50 price with no bids at higher prices, then it takes someone to send a sell order at a price lower or equal to 51,50. This order will not join the ask, since it matches against your bid before getting to the ask queue.

This process may have taken a long time, or may have happened with a single very large sell order that sweeped the book. The idea remains the same regardless.

During Opening and Closing Auctions.

During auction periods orders are matched at a single price. The auction price is usually determine by some variation of 2 basic rules:

1. It fills every market order on both sides of the book.
2. It fills the most shares from all the limit orders in the book.

During the auction, fills on limit orders are optional, while fills on market orders are mandatory. Limit orders are filled depending on the imbalance between buy and sell market orders.

There are some small variations from one market to the next on how they implement this, but they all follow the same basic idea. All orders get executed on a single print and the auction price becomes the official open or closing price for the day.

your order

It sounds like your order was executed during the opening auction, and there probably was a lot of selling interest on the market orders and this interest drove the price down to fill you with a 0.24 price improvement.