Market Impact Model

Market impact is decomposed into two fundamental components:

• Temporary Impact: The transient liquidity cost caused by demanding immediacy. This component reflects the premium paid to attract counterparties and typically decays rapidly after the trade completes, representing the bid-ask bounce and inventory effects.
• Permanent Impact: The lasting price shift caused by the information content of the trade. The market interprets aggressive buying as a potential signal of positive private information, resulting in a permanent price adjustment that does not revert.

The total implementation shortfall of any execution algorithm is the sum of these two components.

The empirically observed relationship between trade size and market impact follows a concave power law with an exponent of approximately 0.5. This means:

• Impact scales with the square root of order size, not linearly
• A trade 4x larger generates only ~2x the impact
• This property holds across asset classes, time periods, and venues

The square-root model, formalized by Almgren et al. (2005), implies that splitting large orders reduces total impact, as the sum of square roots is less than the square root of the sum. This mathematical property underpins all TWAP and VWAP execution strategies.

Market impact is a function of the participation rate—the fraction of total market volume consumed by the executing order:

• Low participation (<5%): Impact is approximately linear with participation rate
• Moderate participation (5-30%): Impact follows the square-root relationship
• High participation (>30%): Impact becomes super-linear as the order exhausts available liquidity and triggers liquidity crises

Calibrating this relationship requires tick-level data to measure the volume-synchronized probability of adverse selection at each participation level.

After a trade executes, the order book does not instantly recover. The resilience of the limit order book determines how quickly liquidity replenishes:

• Exponential decay models: Assume impact decays as I(t) = I₀ × e^(-ρt), where ρ is the resilience parameter
• Power-law decay: Observed in empirical studies, with slower long-term decay than exponential models
• Hawkes process models: Capture the self-exciting nature of order flow, where trades beget more trades

Accurate decay modeling is critical for determining the optimal time between child orders in a sliced execution schedule.

Trading in one instrument can generate price pressure in correlated assets. This cross-impact phenomenon is modeled through a matrix of coefficients:

• Diagonal terms: Direct impact of an asset on itself
• Off-diagonal terms: Spillover impact between correlated pairs (e.g., SPY options affecting SPY shares)
• Lead-lag relationships: Impact propagates with measurable delays across the correlation network

Portfolio-level execution algorithms must optimize across the full cross-impact matrix to minimize total implementation shortfall when trading baskets of correlated instruments.

Market impact models must distinguish between earned spread and adverse selection costs:

• Spread capture: When using limit orders, a trader earns the bid-ask spread by providing liquidity. This offsets impact costs.
• Adverse selection: Limit orders are vulnerable to being picked off by informed traders. The probability of adverse selection increases with order duration and market volatility.
• Fill probability models: Calibrate the trade-off between spread capture and execution certainty, determining the optimal mix of limit and market orders in an execution schedule.

A simulation component that calculates the difference between expected and actual fill prices. In backtesting engines, slippage models incorporate:

• Spread costs: Crossing the bid-ask spread
• Latency effects: Price movement during order transmission
• Market impact: The trade's own footprint on the order book

A robust slippage model prevents overly optimistic backtests by realistically degrading fill prices as order size increases relative to available liquidity.

The quantitative framework for measuring and attributing total execution costs. TCA decomposes costs into:

• Pre-trade estimates: Forecasted impact using models like Almgren-Chriss
• Real-time monitoring: Tracking slippage during execution
• Post-trade attribution: Comparing actual costs against benchmarks

TCA provides the feedback loop for calibrating market impact models and evaluating broker or algorithm performance. It is a regulatory requirement under MiFID II for institutional trading.

A high-fidelity simulation technique that reconstructs historical limit order book depth at each price level. Unlike simple slippage models, order book replay captures:

• Queue position dynamics: Where an order sits in the priority queue
• Liquidity replenishment: How quickly the book refills after trades
• Hidden liquidity: Iceberg orders and dark pool interaction

This granularity is essential for accurately modeling the temporary impact component and testing execution algorithms against realistic microstructure.

A backtesting resolution that replays every individual trade and quote update rather than using aggregated bars. Critical for market impact modeling because:

• Captures intra-spread price movements missed by OHLC data
• Enables realistic fill simulation based on available volume at each price
• Preserves order book state for accurate queue position modeling

Tick-level simulation is computationally intensive but necessary for strategies where latency and microstructure dominate performance, such as high-frequency market making.