Microstructure Models

Exchange-Accurate Cadence Simulation

Unlike generic synthetic data generators that emit perfect metronome ticks, The Aleatoric Engine replicates real exchange behavior.

Rate Limit Simulation

market = HyperSynthReactor(
    symbol="SOL",
    book_update_interval_ms=100,  # Match Binance 100ms snapshot rate
    trade_intensity_base=2.0,      # ~2 trades/sec baseline
)

Burst Mode

Simulate exchange message avalanches during high volatility:

config = SimulationManifest(
    burst_probability=0.05,        # 5% chance of entering burst
    burst_intensity_factor=10.0,   # 10x message rate during burst
)

During a liquidation cascade, message rates spike 10-100x. The engine captures this.

Staleness Simulation

Network jitter and exchange processing delays:

config = SimulationManifest(
    staleness_ms=50.0,  # Mean 50ms lag with log-normal distribution
)

Includes:

• Log-normal jitter distribution (realistic network behavior)
• Occasional massive lag spikes (0.5% probability of 100-1000ms delays)
• Separate timestamp_ms (exchange time) and capture_time_ms (receive time)

L2/L3 Order Book Behavior

Order Book Replenishment

Liquidity providers react to aggressive flow:

market = HyperSynthReactor(
    adverse_selection_strength=0.15,  # 15% depth depletion
    impact_decay_halflife_ms=5000.0,  # 5s recovery
)

Queue Dynamics

• Exponential depth profile: Size decreases exponentially away from best bid/ask
• Volatility-dependent liquidity withdrawal: Higher vol → lower depth
• Toxicity-aware spread widening: Informed flow detection → spreads widen

spread_vol_sensitivity=0.15,        # Volatility impact
spread_toxicity_sensitivity=0.25,   # Informed flow impact

Book Shape Distributions

Real orderbooks don’t have uniform depth. The engine models:

• Power-law depth decay (depth_decay_rate=0.85)
• Volume-weighted microprice calculation
• Realistic bid/ask imbalances

Trade Size Heteroskedasticity

trade_size_alpha=2.5,  # Pareto exponent (lower = fatter tail)
min_trade_size=0.1,
max_trade_size=50.0,

Result: Many small trades (~0.1-1.0 size), occasional whale trades (10-50 size).

Funding Rate Physics

Exchange-Specific Models

The engine models the ACTUAL implementation of each exchange:

Exchange	Interval	Formula	Unique Features
Binance	8h	Premium + Interest Rate	Soft/hard caps (±0.75%/±2%), damping
HyperLiquid	8h	Premium × Velocity	Trend amplification (0.3x-2.5x), ±4% cap
OKX	8h	Premium + Interest (damped)	Threshold filtering
Bybit	8h	Premium + Interest (insurance)	Wide ranges (±2.5%), liquidation spikes
CME	8h	Premium/8 + Interest + Carry	Carry cost (+0.05%)
SGX	4h	Spread/4 + Interest	Conservative 50% application

Spot-Perp-Funding Triangle

Spot Price Process:

• Geometric Brownian Motion (GBM) with configurable drift/volatility
• Jump diffusion for tail events (liquidations, news shocks)

Funding Rate Dynamics:

• Ornstein-Uhlenbeck (OU) mean-reverting process
• Hard bounds to prevent unrealistic rates
• White noise component for micro-jitter

Perpetual Pricing:

Perp Price = Spot × (1 + Funding Rate + Basis Deviation)

Slippage & Impact

Market orders eat through the order book. Large orders suffer slippage exactly as they would in production:

price_impact = weighted_average_price(filled_levels)

No “flat slippage” assumptions—we calculate the weighted average price of filled levels.

Configuration Parameters

Parameter	Description
burst_probability	Chance of entering burst mode
burst_intensity_factor	Message rate multiplier during burst
staleness_ms	Mean network latency
adverse_selection_strength	Depth depletion on aggressive flow
impact_decay_halflife_ms	Recovery time for depleted depth
spread_vol_sensitivity	Spread widening under volatility
spread_toxicity_sensitivity	Spread widening under informed flow
depth_decay_rate	Power-law decay away from touch
trade_size_alpha	Pareto exponent for trade sizes