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FOK order type: can they be market or limit orders?
You can do FOK on both market and limit orders. Normal market orders will partial fill if you want more shares than are being offered, or if someone pulled their order before you get there and now there are fewer shares than you placed a trade for. With a FOK limit order not at the BBO you are shooting in the dark for a quick match, most of the time it does not fill.  This is a commonly used order type for UHFT arbitrage.  Some exchanges will not attempt to cross it for a match if its price is not at, or better than the market price. When the FOK limit order is at the BBO it is essentially a FOK market order.   FYI: Sometimes you have a minimum quantity to fill option, so you can let the order sit on the book until it fills or you cancel.