Market Making: Inventory Management and Optimal Quoting

Module: Fintech AI | Difficulty: Advanced

Avellaneda-Stoikov Model

where = mid-price, = inventory, = risk aversion.

PnL Decomposition

Inventory Risk

import numpy as np

class MarketMaker:
    def __init__(self, gamma, sigma, inventory_limit=100):
        self.gamma = gamma; self.sigma = sigma
        self.inv_limit = inventory_limit; self.inventory = 0
    def optimal_quote(self, mid_price, time_to_close):
        inventory_penalty = self.gamma * self.sigma**2 * self.inventory
        spread = self.gamma * self.sigma**2 * time_to_close
        bid = mid_price - spread/2 - inventory_penalty
        ask = mid_price + spread/2 - inventory_penalty
        return {'bid': bid, 'ask': ask}
    def update_inventory(self, trade, size):
        if trade == 'buy':
            self.inventory += size
        else:
            self.inventory -= size

Research Insight: Optimal market making requires balancing profit from spread against inventory risk. The Avellaneda-Stoikov model provides the optimal quoting strategy under the assumption of Poisson arrivals and permanent impact. In practice, the model is adapted with additional risk controls.