Instant execution fills an order at exactly the price displayed, or rejects/requotes it if that price is no longer available — common with dealing-desk and market-maker brokers. Market execution instead fills the order at the best available price at that moment, whatever it is, without a requote — the standard model for ECN and STP brokers.
Market execution avoids the friction of requotes but exposes the trader to slippage in either direction; instant execution avoids slippage but can mean more frequent requotes during volatile periods.
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Guide
How Execution Models Work: ECN, STP and Market Maker
Market maker, STP and ECN describe where the other side of a trade comes from — and what each model changes about spreads, requotes and order handling.