Algorithmic trading in a microstructural limit order book model

Abergel, Frédéric; Huré, Côme; Pham, Huyên

doi:10.1080/14697688.2020.1729396

Cited by 18 publications

(14 citation statements)

References 39 publications

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“…An 'optimal 'strategy that would lose money in the market would be an indication of poor modelling ! Based on the work in [Hult and Kiessling, 2010] (see also [Abergel et al, 2017] [Bäuerle and Rieder, 2011] for related approach and results), optimal market making strategies are numerically and empirically studied under the various hypotheses corresponding to the models labelled 0 and II introduced in Section 2.4. In the interest of readability, the theoretical framework and main results are recalled in Appendix A, while the current section is devoted to the presentation and discussion of the results.…”

Section: Market Making In Real Marketsmentioning

confidence: 99%

“…these actual microstructural properties of the order book play a fundamental role in assessing the profitability of market making strategies. There now exists an abundant literature on order book modelling, and the reader is referred to [Abergel et al, 2016] for an extensive study of the subject, but, as regards market making strategies -or more general trading strategies, for that matter -only very recent papers such as [Abergel et al, 2017] actually address the market making problem using a full order book model.…”

Section: Introductionmentioning

confidence: 99%

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Order-Book Modeling and Market Making Strategies

Abergel

2018

Mark. Microstructure Liq.

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Market making is one of the most important aspects of algorithmic trading, and it has been studied quite extensively from a theoretical point of view. The practical implementation of socalled "optimal strategies" however suffers from the failure of most order book models to faithfully reproduce the behaviour of real market participants.This paper is twofold. First, some important statistical properties of order driven markets are identified, advocating against the use of purely Markovian order book models. Then, market making strategies are designed and their performances are compared, based on simulation as well as backtesting. We find that incorporating some simple non-Markovian features in the limit order book greatly improves the performances of market making strategies in a realistic context.

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Section: Market Making In Real Marketsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Order-Book Modeling and Market Making Strategies

Abergel

2018

Mark. Microstructure Liq.

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“…More precisely, we postulate that they assume an order book model similar to the one suggested by the Queue-Reactive model [18], see also [1,12,17], in which we restrict to the best bid and ask queues 1 : limit and aggressive orders arrive with certain intensities, when a queue is depleted it is regenerated according to a certain law and possibly after a price move, the spread can take two different values 2 . Importantly, we also take the order book's imbalance into account in the modeling of the different transition probabilities, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…We will actually see that, in certain situations, participants can place aggressive orders or limit orders in the spread just to try to manipulate the order book's dynamics in a favorable way. Note that the dimension of our control space is higher than in [1,17,22,23] since more complex decisions are required to tackle the market making problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal inventory management and order book modeling

Baradel¹,

Bouchard

Evangelista

et al. 2019

ESAIM: ProcS

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We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [12,18,19], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy. . D. Evangelista was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452. ¶ CMAP, École Polytechnique. othmane.mounjid@polytechnique.edu. arXiv:1802.08135v2 [q-fin.TR] 9 Nov 2018 v(t, z) := sup φ∈C(t,z)Remark 3.3. Note that v is bounded from above by 0 by definition. On the other hand, for all E[U (P t,z,0 T , 0, 0, g, i, 0, 0, 0, 0, j)] = e −η(g− j) min i∈[−I * ,I * ] E[U (P t,z,0 T , 0, 0, 0, i, 0, 0, 0, 0, 0)], where P t,z,0 corresponds to the dynamics in the case that the MM does not act on the order book up to T . Moreover, it follows from (3.3) that E[U (P t,z,0 T , 0, 0, 0, i, 0, 0, 0, 0, 0)] ≥ −e ηI * |p b | E[e ηI * (|P t,z,0,b T −p b |+2d+κ) ]where supby Remark 2.1 and the fact that the price can jump only by d when a market event occurs. Thus, v belongs to the class L exp ∞ of functions ϕ such that ϕ/L is bounded, in which The dynamic programming equationThe derivation of the dynamic programming equation is standard, and is based on the dynamic programming principle. We state below the weak version of Bouchard and Touzi [10], we let v * and v * denote the lower-and upper-semicontinuous envelopes of v. Proposition 3.1. Fix (t, z) ∈ [0, T ] × D Z and a family {θ φ , φ ∈ C(t, z)} such that each θ φ is a [t, T ]-valued F t,z,φ -stopping time and Z t,z,φ θ φ L∞ < ∞. Then, sup φ∈C(t,z) E v * (θ φ , Z t,z,φ θ φ ) ≤ v(t, z) ≤ sup φ∈C(t,z)E v * (θ φ , Z t,z,φ θ φ ) .

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“…This nonlinear Feynman-Kac formula can be used to design algorithms based on the numerical approximation of the solution to the constrained BSDE (4.2)-(4.3)-(4.4), and therefore to get probabilistic numerical approximations for the value function of the considered optimal control problem. Recently, numerical schemes for constrained BSDEs have been proposed and analyzed in the diffusive framework, see [23], and in the PDMPs context as well, see [1]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Constrained BSDEs Driven by a Non-Quasi-Left-Continuous Random Measure and Optimal Control of PDMPs on Bounded Domains

Bandini¹

2019

SIAM J. Control Optim.

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We consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. The control problem under study is very general: a pair of controls acts continuously on the deterministic flow and on the two transition measures (in the interior and from the boundary of the domain) describing the jump dynamics of the process. For this class of control problems, the value function can be characterized as the unique viscosity solution to the corresponding fully-nonlinear Hamilton-Jacobi-Bellman equation with a non-local type boundary condition.By means of the recent control randomization method, we are able to provide a probabilistic representation for the value function in terms of a constrained backward stochastic differential equation (BSDE), known as nonlinear Feynman-Kac formula. This result considerably extends the existing literature, where only the case with no jumps from the boundary is considered. The additional boundary jump mechanism is described in terms of a non quasi-left-continuous random measure and induces predictable jumps in the PDMP's dynamics. The existence and uniqueness results for BSDEs driven by such a random measure are non trivial, even in the unconstrained case, as emphasized in the recent work [2].Keywords: Backward stochastic differential equations, optimal control problems, piecewise deterministic Markov processes, non quasi-left-continuous random measure, randomization of controls.MSC 2010: 93E20, 60H10, 60J25.

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Algorithmic trading in a microstructural limit order book model

Cited by 18 publications

References 39 publications

Order-Book Modeling and Market Making Strategies

Order-Book Modeling and Market Making Strategies

Optimal inventory management and order book modeling

Constrained BSDEs Driven by a Non-Quasi-Left-Continuous Random Measure and Optimal Control of PDMPs on Bounded Domains

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