To Cross or Not to Cross the Spread: <i>That Is the Question</i>

Besson, Paul; Pelin, Stéphanie; Lasnier, Matthieu

doi:10.3905/jot.2016.11.4.077

Cited by 2 publications

(6 citation statements)

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“…2.2 Stylized fact 1: the predictive power of the orderbook imbalance Short term price prediction utility. Academic papers (see [Bouchaud et al, 2004] or [Huang et al, 2015]) and brokers' research papers (see [Besson et al, 2016]) document how the sizes at first limits of the public orderbook 2 influence the next price move. It is worthwhile to underline that the identified effects are usually not strong enough to be the source of a statistical arbitrage: the expected value of buying and selling back using accurate predictions based on sizes at first limits does not beat transaction costs (bid-ask spread and fees).…”

Section: Database Presentationmentioning

confidence: 99%

Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency

Lehalle

Mounjid

2017

Mark. Microstructure Liq.

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This paper is split in three parts:¯rst, we use labeled trade data to exhibit how market participants' decisions depend on liquidity imbalance; then, we develop a stochastic control framework where agents monitor limit orders, by exploiting liquidity imbalance, to reduce adverse selection. For limit orders, we need optimal strategies essentially to¯nd a balance between fast execution and avoiding adverse selection: if the price has chances to go down, the probability to be¯lled is high, but it is better to wait a little more to get a better price. In a third part, we show how the added value of exploiting liquidity imbalance is eroded by latency: being able to predict future liquidity consuming°ows is of less use if you do not have enough time to cancel and reinsert your limit orders. There is thus a rationale for market makers to be as fast as possible to reduce adverse selection. Latency costs of our limit order driven strategy can be measured numerically.To authors' knowledge, this paper is the¯rst to make the connection between empirical evidences, a stochastic framework for limit orders including adverse selection, and the cost of latency. Our work is a¯rst step to shed light on the role played by latency and adverse selection in optimal limit order placement.

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Section: Database Presentationmentioning

confidence: 99%

Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency

Lehalle

Mounjid

2017

Mark. Microstructure Liq.

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“…In particular, it can depend on the order book's imbalance, as observed in e.g. [9]. To be consistent with the constraints imposed above, it satisfies:μ…”

Section: Introductionmentioning

confidence: 78%

“…Let us first describe a realistic prior distribution for the evolution of Ẽ. The coefficients we use are inspired from the behavior of the stock Société Générale (CLE FP) 6 and from [9].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The size of the market orders is also assumed to be dependent on the order book imbalance. We use [9,Chart 16 p.10] to estimate that the size of the trade arriving at the ask (if it arrives at the ask), represents a percentage of the queue (that we round to an integer number, by above). Namely, we set fa τi := 0.7 + 0.3 * Imb τi , and assign a (conditional) probability of 60% that the order is of size round[ fa τi * Q a τi ] and the same probability that the executed volume deviates from the latter by one unit (with equal probability to be by one more and one less unit -if quantities are negative or bigger than the size of the queue, we obviously set them to 0 or to the size of the queue).…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Importantly, we also take the order book's imbalance into account in the modeling of the different transition probabilities, see e.g. Besson et al [9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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To Cross or Not to Cross the Spread: That Is the Question

Cited by 2 publications

References 1 publication

Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency

Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency

Optimal inventory management and order book modeling

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