Market Microstructure & Limit Order Book Matching in Quantitative Finance

Continuous double auction markets match buyers and sellers across a discrete price grid ordered by price-time priority ($\text{FIFO}$).

The Limit Order Book Dynamics

Let $b_t(p)$ and $a_t(p)$ denote bid and ask queue depths at price level $p$:

Order book imbalance $\rho_t$ provides short-term directional alpha:

Stochastic Jump-Diffusion Asset Pricing

The continuous asset price dynamic governed by Merton's jump-diffusion SDE:

Where $W_t$ is a standard Brownian motion and $N_t$ is a Poisson process with jump intensity $\lambda$.

type Order struct {
	ID        int64
	Price     uint64 // Fixed-point integer (e.g. $100.50 -> 1005000)
	Quantity  uint64
	Timestamp int64
}

type OrderBook struct {
	Bids map[uint64]*RingQueue
	Asks map[uint64]*RingQueue
}

Price discovery occurs in sub-microsecond intervals where memory latency governs execution advantage.