Francesco Finardi

An Extended Avellaneda-Stoikov Market Making Model

Abstract: I present a synthetic simulation study of the Avellaneda-Stoikov market making model augmented with the three extensions drawn from Fushimi, Gonzalez~Rojas, and Herman: (i) a three-state order book management algorithm that handles one-sided and two-sided quoting with waiting and refresh logic; (ii) an inventory-dependent dynamic order sizing model [math]\varphi(q_t)[/math] that exponentially reduces size in the direction of excess inventory; and (iii) a Bernoulli-Gamma order execution model that allows partial fills. These are combined with a time-varying order arrival intensity [math]\alpha(t)[/math] exhibiting the empirical U-shaped intraday pattern documented by Cartea, Jaimungal, and Penalva. Unlike the original study, which calibrates parameters to five real equities, I evaluate the integrated strategy across three synthetic volatility regimes ([math]\sigma \in {0.5, 2.0, 5.0}[/math]) using 10.000 Monte Carlo simulations per scenario, each representing a 6.5-hour trading day at 5-second resolution. I benchmark the extended “optimal” strategy against a naive fixed-spread baseline. Results confirm that the optimal strategy consistently dominates on a risk-adjusted basis, with Sharpe ratio improvements of up to 81% in the most volatile regime, driven primarily by the inventory-aware reservation price and a volatility-adjusted order size cap that I introduce as an additional extension.

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Keywords: Market Making, Avellaneda-Stoikov Model, High-Frequency Trading (HFT), Inventory Management, Monte Carlo Simulation