A Complete Guide to the Order Matching Engine

The order matching engine is the heart of any trading system. It consists of several key components, including matching algorithms, data management, and communication interfaces. Its core function is to match buy and sell orders from market participants, execute trades, and generate transaction records. Every day, vast amounts of liquidity flow through financial markets, and it’s the order matching engine that ensures this process is executed efficiently.

Without an order matching engine, a trading platform—regardless of asset class (be it forex, commodities, equities, or CFDs)—cannot facilitate real transactions. In fact, all other modules within a trading system effectively serve to support the order matching engine.

A Brief History of Order Matching

The concept of order matching dates back to the 19th century, when trading was done manually through an open outcry system. On exchanges like the New York Stock Exchange (NYSE), traders would shout buy and sell orders on the trading floor to execute trades—a method that was loud but effective at the time.

With advancements in electronic technology, markets gradually transitioned to automated systems. In 1971, NASDAQ launched the world’s first electronic order matching engine, where computers, rather than people, handled trade execution. This innovation dramatically increased speed, efficiency, and scalability, laying the groundwork for modern electronic trading.

How the Order Matching Process Works

Order Book Management

The order book is a critical component of the order matching engine, tracking all currently open limit orders.

• Buy Order Book: Lists bids from highest to lowest. Higher bids receive execution priority.
• Sell Order Book: Lists asks from lowest to highest. Lower asks are filled first.

Proper management of the order book is vital for maintaining market liquidity and supporting the price discovery process. The order book must be updated in real time as market conditions evolve.

Market Orders vs. Limit Orders

Market Order

• Executes immediately at the best available price.
• Prioritizes speed and execution certainty over price control.
• May suffer from slippage in low-liquidity conditions.

Limit Order

• Specifies a minimum (sell) or maximum (buy) price at which the trader is willing to transact.
• Enters the order book and executes only when the market reaches the target price.
• Ensures price control, but execution is not guaranteed.

Common Order Matching Algorithms (with Examples)

Here are three widely used order matching algorithms, with sample implementations for each:

1. Price-Time Priority (FIFO)

This is the most common algorithm used in modern markets. Orders are prioritized first by price (better prices matched first), and then by time (earlier orders take precedence at the same price level).

import heapq

class Order:
    def __init__(self, order_id, order_type, price, quantity):
        self.order_id = order_id
        self.order_type = order_type  # 'buy' or 'sell'
        self.price = price
        self.quantity = quantity
        self.timestamp = None

    def __lt__(self, other):
        if self.order_type == 'buy':
            # For buy orders, higher prices have priority; if prices are equal, earlier orders have priority
            return (self.price, -self.timestamp) > (other.price, -other.timestamp)
        else:
            # For sell orders, lower prices have priority; if prices are equal, earlier orders have priority
            return (self.price, self.timestamp) < (other.price, other.timestamp)

class OrderBook:
    def __init__(self):
        self.buy_orders = []  # Max-heap for buy orders (negative prices for max-heap)
        self.sell_orders = []  # Min-heap for sell orders
        self.timestamp_counter = 0

    def add_order(self, order):
        order.timestamp = self.timestamp_counter
        self.timestamp_counter += 1

        if order.order_type == 'buy':
            heapq.heappush(self.buy_orders, order)
        else:
            heapq.heappush(self.sell_orders, order)

    def match_orders(self):
        matches = []

        while self.buy_orders and self.sell_orders:
            highest_buy_order = self.buy_orders[0]
            lowest_sell_order = self.sell_orders[0]

            if highest_buy_order.price >= lowest_sell_order.price:
                quantity_to_trade = min(highest_buy_order.quantity, lowest_sell_order.quantity)
                matches.append((highest_buy_order.order_id, lowest_sell_order.order_id, quantity_to_trade))

                highest_buy_order.quantity -= quantity_to_trade
                lowest_sell_order.quantity -= quantity_to_trade

                if highest_buy_order.quantity == 0:
                    heapq.heappop(self.buy_orders)
                if lowest_sell_order.quantity == 0:
                    heapq.heappop(self.sell_orders)
            else:
                break

        return matches

# Example usage
order_book = OrderBook()

# Add some buy and sell orders
order_book.add_order(Order(1, 'buy', 101, 10))
order_book.add_order(Order(2, 'buy', 102, 5))
order_book.add_order(Order(3, 'sell', 100, 8))
order_book.add_order(Order(4, 'sell', 99, 10))

# Match orders
matches = order_book.match_orders()

for match in matches:
    print(f"Matched Buy Order {match[0]} with Sell Order {match[1]} for {match[2]} units")

2. Pro-Rata Allocation

Orders at the same price level are matched proportionally based on order size. Larger orders are allocated more volume. This approach is often used in futures exchanges.

import heapq
from collections import defaultdict

class Order:
    def __init__(self, order_id, order_type, price, quantity):
        self.order_id = order_id
        self.order_type = order_type  # 'buy' or 'sell'
        self.price = price
        self.quantity = quantity
        self.timestamp = None

class OrderBook:
    def __init__(self):
        self.buy_orders = defaultdict(list)  # Buy orders grouped by price
        self.sell_orders = defaultdict(list)  # Sell orders grouped by price
        self.timestamp_counter = 0

    def add_order(self, order):
        order.timestamp = self.timestamp_counter
        self.timestamp_counter += 1

        if order.order_type == 'buy':
            self.buy_orders[order.price].append(order)
        else:
            self.sell_orders[order.price].append(order)

    def match_orders(self):
        matches = []

        # Sort buy and sell prices
        buy_prices = sorted(self.buy_orders.keys(), reverse=True)
        sell_prices = sorted(self.sell_orders.keys())

        while buy_prices and sell_prices:
            highest_buy_price = buy_prices[0]
            lowest_sell_price = sell_prices[0]

            if highest_buy_price >= lowest_sell_price:
                buy_orders_at_price = self.buy_orders[highest_buy_price]
                sell_orders_at_price = self.sell_orders[lowest_sell_price]

                # Calculate total buy and sell quantities at this price
                total_buy_quantity = sum(order.quantity for order in buy_orders_at_price)
                total_sell_quantity = sum(order.quantity for order in sell_orders_at_price)

                # Determine the amount to trade based on the smaller side
                quantity_to_trade = min(total_buy_quantity, total_sell_quantity)

                # Pro-rata allocation for buy and sell orders
                for order in buy_orders_at_price:
                    proportion = order.quantity / total_buy_quantity
                    traded_quantity = quantity_to_trade * proportion
                    matches.append((order.order_id, lowest_sell_price, traded_quantity))
                    order.quantity -= traded_quantity

                for order in sell_orders_at_price:
                    proportion = order.quantity / total_sell_quantity
                    traded_quantity = quantity_to_trade * proportion
                    matches.append((order.order_id, highest_buy_price, traded_quantity))
                    order.quantity -= traded_quantity

                # Remove fully matched orders
                self.buy_orders[highest_buy_price] = [o for o in buy_orders_at_price if o.quantity > 0]
                self.sell_orders[lowest_sell_price] = [o for o in sell_orders_at_price if o.quantity > 0]

                if not self.buy_orders[highest_buy_price]:
                    del self.buy_orders[highest_buy_price]
                    buy_prices.pop(0)

                if not self.sell_orders[lowest_sell_price]:
                    del self.sell_orders[lowest_sell_price]
                    sell_prices.pop(0)
            else:
                break

        return matches

# Example usage
order_book = OrderBook()

# Add some buy and sell orders
order_book.add_order(Order(1, 'buy', 100, 10))
order_book.add_order(Order(2, 'buy', 100, 20))
order_book.add_order(Order(3, 'sell', 100, 15))
order_book.add_order(Order(4, 'sell', 100, 5))

# Match orders
matches = order_book.match_orders()

for match in matches:
    print(f"Order {match[0]} matched at price {match[1]} for {match[2]:.2f} units")

3. Hybrid Matching

Combines elements of price-time priority and pro-rata allocation. The engine dynamically balances execution logic depending on market structure or participant behavior, offering a flexible and fair solution.

import heapq
from collections import defaultdict

class Order:
    def __init__(self, order_id, order_type, price, quantity):
        self.order_id = order_id
        self.order_type = order_type  # 'buy' or 'sell'
        self.price = price
        self.quantity = quantity
        self.timestamp = None

    def __lt__(self, other):
        return self.timestamp < other.timestamp

class OrderBook:
    def __init__(self):
        self.buy_orders = defaultdict(list)  # Buy orders grouped by price
        self.sell_orders = defaultdict(list)  # Sell orders grouped by price
        self.timestamp_counter = 0

    def add_order(self, order):
        order.timestamp = self.timestamp_counter
        self.timestamp_counter += 1

        if order.order_type == 'buy':
            heapq.heappush(self.buy_orders[order.price], order)
        else:
            heapq.heappush(self.sell_orders[order.price], order)

    def match_orders(self):
        matches = []

        # Sort buy and sell prices
        buy_prices = sorted(self.buy_orders.keys(), reverse=True)
        sell_prices = sorted(self.sell_orders.keys())

        while buy_prices and sell_prices:
            highest_buy_price = buy_prices[0]
            lowest_sell_price = sell_prices[0]

            if highest_buy_price >= lowest_sell_price:
                buy_orders_at_price = self.buy_orders[highest_buy_price]
                sell_orders_at_price = self.sell_orders[lowest_sell_price]

                # Calculate total buy and sell quantities at this price
                total_buy_quantity = sum(order.quantity for order in buy_orders_at_price)
                total_sell_quantity = sum(order.quantity for order in sell_orders_at_price)

                # Determine the amount to trade based on the smaller side
                quantity_to_trade = min(total_buy_quantity, total_sell_quantity)

                # Priority based matching and then pro-rata allocation
                while quantity_to_trade > 0 and buy_orders_at_price and sell_orders_at_price:
                    buy_order = buy_orders_at_price[0]
                    sell_order = sell_orders_at_price[0]

                    if buy_order.quantity <= sell_order.quantity:
                        matches.append((buy_order.order_id, sell_order.order_id, buy_order.quantity))
                        sell_order.quantity -= buy_order.quantity
                        quantity_to_trade -= buy_order.quantity
                        heapq.heappop(buy_orders_at_price)
                        if sell_order.quantity == 0:
                            heapq.heappop(sell_orders_at_price)
                    else:
                        matches.append((buy_order.order_id, sell_order.order_id, sell_order.quantity))
                        buy_order.quantity -= sell_order.quantity
                        quantity_to_trade -= sell_order.quantity
                        heapq.heappop(sell_orders_at_price)
                        if buy_order.quantity == 0:
                            heapq.heappop(buy_orders_at_price)

                # Remove empty price levels
                if not buy_orders_at_price:
                    del self.buy_orders[highest_buy_price]
                    buy_prices.pop(0)

                if not sell_orders_at_price:
                    del self.sell_orders[lowest_sell_price]
                    sell_prices.pop(0)

            else:
                break

        return matches

# Example usage
order_book = OrderBook()

# Add some buy and sell orders
order_book.add_order(Order(1, 'buy', 100, 15))
order_book.add_order(Order(2, 'buy', 100, 25))
order_book.add_order(Order(3, 'sell', 100, 30))
order_book.add_order(Order(4, 'sell', 100, 10))

# Match orders
matches = order_book.match_orders()

for match in matches:
    print(f"Buy Order {match[0]} matched with Sell Order {match[1]} for {match[2]:.2f} units")