Optimal liquidity-based trading tactics

Lehalle, Charles‐Albert; Mounjid, Othmane; Rosenbaum, Mathieu

doi:10.48550/arxiv.1803.05690

Cited by 4 publications

(9 citation statements)

References 19 publications

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“…Assumption 2 ensures that both the size of the first limits and the spread tend to decrease when they become too large. Same kind of hypothesis are used in [15,26] but when the order book dynamic is Markov.…”

Section: Assumption 2 (Negative Drift)mentioning

confidence: 99%

“…with c(e), d(e) and φ * defined in Assumption 1, i ∈ B, x ∈ W 0 and C bound defined in Assumption (2). Similar assumptions are considered in [15,26] in the Markov case.…”

Section: Assumption 2 (Negative Drift)mentioning

confidence: 99%

“…Here we focus on the first limits to reduce the dimension of the state space and keep a tractable model 1 . Finally, we use a general approach to infer the behaviour of the price process from that of (U n ), in the spirit of [16,26], see Section 4 for the detailed formulation. We define the non-linear Hawkes-Markovian arrival rate λ t (e) of an order book event e (e containing the identity of the involved agent) at time t ∈ R + as follows:…”

Section: Introductionmentioning

confidence: 99%

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From asymptotic properties of general point processes to the ranking of financial agents

Mounjid,

Rosenbaum,

Saliba

2019

Preprint

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We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity and diffusivity of such system. Then we provide closed form formulas for various quantities of interest: stationary distribution of the best bid and ask quantities, spread, liquidity fluctuations and price volatility. These formulas are expressed in terms of individual order flows of market participants. Our approach enables us to establish a ranking methodology for the market makers with respect to the quality of their trading.

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Section: Assumption 2 (Negative Drift)mentioning

confidence: 99%

“…with c(e), d(e) and φ * defined in Assumption 1, i ∈ B, x ∈ W 0 and C bound defined in Assumption (2). Similar assumptions are considered in [15,26] in the Markov case.…”

Section: Assumption 2 (Negative Drift)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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From asymptotic properties of general point processes to the ranking of financial agents

Mounjid,

Rosenbaum,

Saliba

2019

Preprint

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“…This provides a characterization of the value function in terms of a fixed point dynamic programming equation. Jacquier and Liu in [JL18] recently followed a similar idea to solve an optimal liquidation problem, while Baradel et al [BBEM18] and Lehalle et al [LOR18] also tackled this problem of reward functional maximization in a micro-structure model of order book framework.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic trading in a microstructural limit order book model

Abergel

Huré

Pham

2020

Quantitative Finance

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We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (order book). In this context, the limit orders, market orders, and cancel orders arrivals in the order book are modeled as Cox point processes with intensities that only depend on the state of the order book. These are high-dimensional models which are realistic from a micro-structure point of view and have been recently developed in the literature. In this context, we consider a market maker who stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price, and identifies the strategies that maximize her P&L penalized by her inventory.We apply the theory of Markov Decision Processes and dynamic programming method to characterize analytically the solutions to our optimal market making problem. The second part of the paper deals with the numerical aspect of the high-dimensional trading problem. We use a control randomization method combined with quantization method to compute the optimal strategies. Several computational tests are performed on simulated data to illustrate the efficiency of the computed optimal strategy. In particular, we simulated an order book with constant/ symmetric/ asymmetrical/ state dependent intensities, and compared the computed optimal strategy with naive strategies.

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“…The main objective of the present paper is to propose a flexible order book dynamics model close to the one of [12,18,19,23], construct a first building block towards a realistic order book modeling, and try to better understand the various regimes related to the presence of different market participants. Instead of considering a pure statistical dynamics as in e.g.…”

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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Optimal liquidity-based trading tactics

Cited by 4 publications

References 19 publications

From asymptotic properties of general point processes to the ranking of financial agents

From asymptotic properties of general point processes to the ranking of financial agents

Algorithmic trading in a microstructural limit order book model

Optimal inventory management and order book modeling

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