Execution Algorithms: Minimizing Market Impact

Module: Fintech AI | Difficulty: Advanced

Market Impact Model

Optimal Execution

Implementation Shortfall

import numpy as np

class OptimalExecution:
    def __init__(self, total_shares, urgency, market_params):
        self.total = total_shares; self.urgency = urgency
        self.gamma = market_params['gamma']
        self.sigma = market_params['sigma']
        self.v_adv = market_params['v_adv']
    def almgren_chriss_optimal(self, n_periods):
        kappa = self.urgency
        schedule = []
        for t in range(n_periods):
            remaining = self.total * np.sinh(kappa * (n_periods - t)) / np.sinh(kappa * n_periods)
            schedule.append(max(0, remaining))
        return schedule

Research Insight: The Almgren-Chriss model provides the optimal execution trajectory by balancing market impact (trading too fast) against timing risk (trading too slow). The urgency parameter controls this trade-off based on the trader's risk aversion.