Market Impact Decay Function

Market impact decay functions are essential for modeling transaction costs in high-frequency and algorithmic trading strategies. When a trader executes a sizable order, it typically moves the market price adversely (temporary impact) and may also shift the equilibrium price level (permanent impact). The decay function captures how quickly this impact reverts, with temporal decay driven by order book replenishment, information dissemination, and inventory rebalancing by market makers. In insider trading detection and quant scoring contexts, understanding decay dynamics helps identify anomalous execution patterns, quantify the true costs of surveillance trades, and assess whether trades on material nonpublic information exhibit unusual speed or impact persistence.

Empirically, market impact decay often follows a power law or exponential profile. Common functional forms include I(t) = I0 * t^(-alpha) for power law decay or I(t) = I0 * exp(-lambda * t) for exponential decay, where I0 is initial impact, t is elapsed time, and alpha or lambda are decay parameters estimated from trade data. The half-life of impact (time for impact to fall to 50% of initial value) serves as a practical metric for liquidity assessment. In regulatory and compliance monitoring, anomalously slow decay or persistent impact may signal information leakage, coordinated trading, or manipulation, warranting escalation to market abuse investigation teams.