Algorithmic trading in a microstructural limit order book model

Abergel, Frédéric; Huré, Côme; Pham, Huyên

doi:10.48550/arxiv.1705.01446

Cited by 2 publications

(5 citation statements)

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“…• When δP = 2d: Limit orders of size L b, 1 2 i ∈ N at the bid or of size L a, 1 2 i ∈ N at the ask: the order is placed inside the spread, at the price P b + d = P a − d, this generates a new queue at the bid or at the ask, of size L b, 1 2 i or L a, 1 2 i , and a price move.…”

Section: General Order Book Presentation and Priors Of The Market Par...mentioning

confidence: 99%

“…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%

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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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Section: General Order Book Presentation and Priors Of The Market Par...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal inventory management and order book modeling

Baradel¹,

Bouchard

Evangelista

et al. 2019

ESAIM: ProcS

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“…Nevertheless, it has been established, see e.g. [Abergel et al, 2016][Lu andAbergel, 2017] for some in-depth empirical studies, that the nature of past events actually influence the order flow and, therefore, the future states of the LOB.…”

Section: The Role Of Limit Removal Ordersmentioning

confidence: 99%

“…This approach, departing from the purely Markovian case, is based on empirical observations and will be shown to provide a more realistic and useful modelling framework. In a different mathematical setting, a similar reasoning is at the root of Hawkes-process-based order book models such as studied in [Lu andAbergel, 2017][Abergel andJedidi, 2015]. The paper is organized as follows: Section 2 presents the rationale and the calibration of the enriched queue reactive model that improve the performances of the initial model of [Huang et al, 2015].…”

Section: Introductionmentioning

confidence: 99%

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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Algorithmic trading in a microstructural limit order book model

Cited by 2 publications

References 0 publications

Optimal inventory management and order book modeling

Optimal inventory management and order book modeling

Order-Book Modeling and Market Making Strategies

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