Macroscopic Market Making
Macroscopic Market Making
This paper introduces a macroscopic market making model that generalizes the Avellaneda-Stoikov framework by modeling order flows as continuous processes rather than discrete point processes. This shift allows the model to bridge the gap between market making and optimal execution problems, as it aligns with the order rate concept used in execution literature. The model is analyzed through three progressively complex problems: first with Markovian noise and linear intensity functions, then with non-Markovian noise and general non-linear intensities, and finally with unbounded coefficients. For each setting, the optimal control problem is transformed into either a PDE or an FBSDE, and well-posedness is established to guarantee existence and uniqueness of the optimal strategy. The paper also explores applications, showing that the macroscopic solution approximates the average of microstructural solutions, that price impact emerges as concave, and that the model can be linked to optimal execution by interpreting the market maker's quoting strategy as a permanent price impact function. Numerical simulations support these findings.
Highlights
- 1Proposes a macroscopic market making model that replaces discrete point processes with continuous order flows, bridging market making and optimal execution.
- 2Extends analysis from Markovian to non-Markovian noise and from linear to non-linear intensity functions, covering bounded and unbounded coefficients.
- 3Establishes existence and uniqueness of optimal control via well-posedness of HJB equations and Lipschitz/non-Lipschitz FBSDEs.
- 4Demonstrates connections to Avellaneda-Stoikov model, concave price impact, and optimal execution through applications and numerical simulations.
Methods
- MDynamic programming principle and Hamilton-Jacobi-Bellman (HJB) equations for Markovian settings.
- MStochastic maximum principle and forward-backward stochastic differential equations (FBSDEs) for non-Markovian settings.
- MTruncation functions and decoupling method for Lipschitz FBSDEs; convex-analytic approach and monotonic sequences for non-Lipschitz FBSDEs.
Results
- ROptimal quoting strategies are derived for three problem settings: Markovian linear, non-Markovian non-linear, and non-Markovian unbounded coefficients.
- RThe macroscopic model's solution approximates the average of Avellaneda-Stoikov solutions, with differences vanishing as tick size approaches zero.
- RConcave price impact is explicitly derived in simple cases and demonstrated via simulations in general settings.
- RA link between market making and optimal execution is established, where permanent price impact is replaced by the market maker's quoting strategy.
Analyze Paper
Generate insights from "Macroscopic Market Making".