Performative Market Making
Performative Market Making
This paper introduces a mathematical framework for performativity in financial markets, focusing on market making. The authors model the asset mid-price as mean-reverting to a reference process representing the valuation implied by dominant trading strategies, creating a feedback loop. They derive closed-form solutions for a performativity-aware market maker who optimally responds to the endogenous price drift generated by competitors using classical strategies (e.g., Avellaneda-Stoikov). The performatively optimal strategy can reverse trading incentives compared to classical optimality, e.g., selling when the classical strategy buys. The paper also defines performative stability as a fixed point where the strategy remains optimal under the price process it induces, and shows that under linear utility the only stable strategy is quoting at the current mid-price. Simulations confirm that performativity-aware strategies consistently outperform classical baselines as the performativity parameter increases, highlighting the importance of accounting for model-induced feedback in modern markets.
Highlights
- 1First quantitative model of performativity in financial markets, embedding model-driven valuations into price dynamics.
- 2Closed-form solutions for performatively optimal market-making strategies that exploit endogenous price drift.
- 3Proof of existence of a performatively stable state (fixed point) where strategies are self-consistent.
- 4Demonstration that performativity-aware strategies can outperform classical Avellaneda-Stoikov baselines.
Methods
- MStochastic optimal control with Hamilton-Jacobi-Bellman (HJB) equations for market making.
- MPerformative price process modeled as an Ornstein-Uhlenbeck process with time-varying drift from reference strategies.
- MFixed-point analysis for performative stability (OptMM operator).
- MSimulation-based empirical validation of strategy performance.
Results
- RPerformatively optimal reservation price differs from classical optimal price, with phase transitions in quoting behavior.
- RPerformatively stable strategy under linear utility is the trivial reservation price equal to the current mid-price.
- RPerformativity-aware strategies outperform classical strategies as performativity parameter ϵ increases.
- RRepeated re-optimization does not generally converge unless a performatively stable fixed point is reached.
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