Market Microstructure & Limit Order Book Matching in Quantitative Finance

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 $p$:

$\text{Mid-Price: } S_t = \frac{p_a^{(1)} + p_b^{(1)}}{2}, \quad \text{Spread: } \delta_t = p_a^{(1)} - p_b^{(1)}$

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

$\rho_t = \frac{V_b^{(1)} - V_a^{(1)}}{V_b^{(1)} + V_a^{(1)}} \in [-1, 1]$

Stochastic Jump-Diffusion Asset Pricing

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

$dS_t = \mu S_t dt + \sigma S_t dW_t + S_{t^-} d\left(\sum_{i=1}^{N_t} (Y_i - 1)\right)$

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

goCopy
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.