papers/lux-ats-architecture/sections/05-order-matching.tex

\section{Order Matching}
\label{sec:matching}

\subsection{Matching Engine}

The matching engine implements price-time priority for continuous order matching:

\begin{lstlisting}[language=Go,caption={Matching engine core.}]
type MatchEngine struct {
    books map[SecurityID]*OrderBook
    mu    sync.RWMutex
}

type OrderBook struct {
    Bids *PriorityQueue // max-heap by price, FIFO by time
    Asks *PriorityQueue // min-heap by price, FIFO by time
}

func (e *MatchEngine) Match(secID SecurityID) []Execution {
    e.mu.Lock()
    defer e.mu.Unlock()

    book := e.books[secID]
    var executions []Execution

    for book.Bids.Len() > 0 && book.Asks.Len() > 0 {
        bestBid := book.Bids.Peek()
        bestAsk := book.Asks.Peek()

        if bestBid.Price.LessThan(bestAsk.Price) {
            break
        }

        qty := min(bestBid.Remaining, bestAsk.Remaining)
        price := bestAsk.Price // price-time priority: aggressor pays

        executions = append(executions, Execution{
            BuyOrder:  bestBid.ID,
            SellOrder: bestAsk.ID,
            Quantity:  qty,
            Price:     price,
            Timestamp: time.Now().UTC(),
        })

        bestBid.Remaining -= qty
        bestAsk.Remaining -= qty

        if bestBid.Remaining == 0 { book.Bids.Pop() }
        if bestAsk.Remaining == 0 { book.Asks.Pop() }
    }
    return executions
}
\end{lstlisting}

\subsection{Order Types}

The ATS supports the following order types, consistent with standard equity market conventions:

\begin{itemize}[nosep]
  \item \textbf{Limit}: Execute at specified price or better.
  \item \textbf{Market}: Execute immediately at best available price.
  \item \textbf{IOC} (Immediate-or-Cancel): Fill what is available, cancel remainder.
  \item \textbf{GTC} (Good-Till-Cancelled): Remain on book until filled or cancelled.
  \item \textbf{GTD} (Good-Till-Date): Remain on book until specified date.
  \item \textbf{RFQ} (Request-for-Quote): Solicit quotes from registered market makers.
\end{itemize}