Closed-form Approximations in Multi-asset Market Making

Bergault, Philippe; Evangelista, David; Guéant, Olivier; Vieira, D.A.G.

doi:10.1080/1350486x.2021.1949359

Cited by 12 publications

(9 citation statements)

References 24 publications

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“…The AS model generates bid and ask quotes that aim to maximize the market maker’s P&L profile for a given level of inventory risk the agent is willing to take, relying on certain assumptions regarding the microstructure and stochastic dynamics of the market. Extensions to the AS model have been proposed, most notably the Guéant-Lehalle-Fernandez-Tapia approximation [ 5 ], and in a recent variation of it by Bergault et al [ 6 ], which are currently used by major market making agents. Nevertheless, in practice, deviations from the model scenarios are to be expected.…”

Section: Background: the Avellaneda-stoikov Proceduresmentioning

confidence: 99%

A reinforcement learning approach to improve the performance of the Avellaneda-Stoikov market-making algorithm

Marín

Vera²,

Eduardo³

2022

PLoS ONE

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Market making is a high-frequency trading problem for which solutions based on reinforcement learning (RL) are being explored increasingly. This paper presents an approach to market making using deep reinforcement learning, with the novelty that, rather than to set the bid and ask prices directly, the neural network output is used to tweak the risk aversion parameter and the output of the Avellaneda-Stoikov procedure to obtain bid and ask prices that minimise inventory risk. Two further contributions are, first, that the initial parameters for the Avellaneda-Stoikov equations are optimised with a genetic algorithm, which parameters are also used to create a baseline Avellaneda-Stoikov agent (Gen-AS); and second, that state-defining features forming the RL agent’s neural network input are selected based on their relative importance by means of a random forest. Two variants of the deep RL model (Alpha-AS-1 and Alpha-AS-2) were backtested on real data (L2 tick data from 30 days of bitcoin–dollar pair trading) alongside the Gen-AS model and two other baselines. The performance of the five models was recorded through four indicators (the Sharpe, Sortino and P&L-to-MAP ratios, and the maximum drawdown). Gen-AS outperformed the two other baseline models on all indicators, and in turn the two Alpha-AS models substantially outperformed Gen-AS on Sharpe, Sortino and P&L-to-MAP. Localised excessive risk-taking by the Alpha-AS models, as reflected in a few heavy dropdowns, is a source of concern for which possible solutions are discussed.

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Section: Background: the Avellaneda-stoikov Proceduresmentioning

confidence: 99%

A reinforcement learning approach to improve the performance of the Avellaneda-Stoikov market-making algorithm

Marín

Vera²,

Eduardo³

2022

PLoS ONE

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“…The running penalty forces him to mean-revert his inventories to zero. We now state the main proposition of Bergault et al (2020) that provides a closed form approximation of V (t, q), and refer to this article for the proof.…”

Section: Market-makingmentioning

confidence: 99%

“…We propose to use the gradient of an approximation of the value function of the optimal market-making problem on OTC markets as the effective microstructure alphas for the optimal market-making problem in order books. To this end, we borrow the OTC framework of Bergault et al (2020) and recall their modeling assumptions briefly.…”

Section: The Long-term Objective Functionmentioning

confidence: 99%

“…, d}, the point processes N i,b t , N i,a t denote the total number of bid and ask transactions between 0 and t on asset i. Their intensities are given by Λ i,b (δ i,b t ), Λ i,a (δ i,a t ) where the functions Λ i,b , Λ i,a satisfy some technical conditions, see Bergault et al (2020) for details. These conditions are sufficiently general to allow the use of several form of intensity such as exponential, logistic, SU Johnson etc.…”

Section: The Long-term Objective Functionmentioning

confidence: 99%

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Optimal trading without optimal control

Baldacci¹,

Benvéniste²,

Ritter³

2020

Preprint

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A hypothetical risk-neutral agent who trades to maximize the expected profit of the next trade will approximately exhibit long-term optimal behavior as long as this agent uses the vector p = ∇V (t, x) as effective microstructure alphas, where V is the Bellman value function for a smooth relaxation of the problem. Effective microstructure alphas are the steepest-ascent direction of V , equal to the generalized momenta in a dual Hamiltonian formulation. This simple heuristics has wide-ranging practical implications; indeed, most utility-maximization problems that require implementation via discrete limit-order-book markets can be treated by our method. * Bastien Baldacci gratefully acknowledge the financial support of the ERC Grant 679836 Staqamof and would like to thank Iuliia Manziuk (Ecole Polytechnique) for fruitful discussions.

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“…In all these articles, the authors consider a risk-adjusted expectation instead of a CARA utility function, which leads to the same optimal quotes with a suitable transformation of the intensity functions, see Manziuk [41]. More recently, multi-asset market-making has been addressed through reinforcement learning, see Guéant and Manziuk [30], and dimensionality reduction techniques, see Bergault and Guéant [10], Bergault, Evangelista, Guéant, and Vieira [11], or Baldacci, Bergault, and Guéant [5] for the special case of option market-making. All these models are well-suited for OTC markets and for order-driven markets in the case of small tick assets, but are not straightforwardly applicable to design market-making strategies on order books with a large tick size, where the control process lies in a discrete tick grid.…”

Section: Introductionmentioning

confidence: 99%

A mean-field game of market-making against strategic traders

Baldacci¹,

Bergault²,

Possamaï³

2022

Preprint

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We design a market-making model à la Avellaneda and Stoikov in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers' behaviour, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB-Fokker-Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviours for the market-takers and takes into account the impact of their strategies on the price process.

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Closed-form Approximations in Multi-asset Market Making

Cited by 12 publications

References 24 publications

A reinforcement learning approach to improve the performance of the Avellaneda-Stoikov market-making algorithm

A reinforcement learning approach to improve the performance of the Avellaneda-Stoikov market-making algorithm

Optimal trading without optimal control

A mean-field game of market-making against strategic traders

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