Buy Low, Sell High: A High Frequency Trading Perspective

Cartea, Álvaro; Jaimungal, Sebastian; Ricci, Jason

doi:10.1137/130911196

Cited by 132 publications

(24 citation statements)

References 17 publications

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“…The idea then is to maximize the profit by playing with the spread between the bid and ask prices, while controlling the inventory risk and the execution risk. See for example, Avelaneda and Stoikov (2008) [8], Bayraktar and Ludkovski (2012) [9], Cartea and Jaimungal (2013) [14], Cartea, Jaimugal, and Ricci (2011) [15], Veraarta (2010) [49], Guilbaud and Pham (2011) [29], Guéant, Lehalla, and Tapia (2012) [28], and Horst, Lehalle and Li (2013) [33]. There are also order scheduling problems especially when orders can be placed in different exchanges with different fee structures.…”

Section: Summary and Discussionmentioning

confidence: 99%

Optimal Placement in a Limit Order Book

Larrard

Ruan

2013

SSRN Journal

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This paper proposes and studies an optimal placement problem in a limit order book. Two simple models are proposed: one with price impact and one without price impact. For the first model, optimal placement strategies for both single-period and multi-period cases are derived. For the second model, it is shown that the optimal strategy never mixes market orders and (best) limit orders; in particular, with special choices of parameters, the optimal strategy reduces to the VWAP type of Bertsimas and Lo (1998) for the optimal execution problem.

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Section: Summary and Discussionmentioning

confidence: 99%

Optimal Placement in a Limit Order Book

Larrard

Ruan

2013

SSRN Journal

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“…For this purpose, we introduce a compound Poisson model for trades processes, which can be fitted to a large class of real‐world execution processes, since we make few assumptions about the distributions of execution volumes. From a practical trading point of view, we allow the HFT to input predictive information about price evolution into the strategy, so that our algorithm can be seen as an information‐driven HFT strategy (this situation is sometimes called HFT with superior information; see Cartea, Jaimungal, and Ricci ). We derive the dynamic programming equation (DPE) corresponding to this mixed impulse/regular control problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal High‐frequency Trading in a Pro Rata Microstructure With Predictive Information

Guilbaud

Pham

2013

Mathematical Finance

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We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation.The optimal trading problem is studied by stochastic control and dynamic programming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.Keywords: Market making, limit order book, pro-rata microstructure, inventory risk, marked point process, stochastic control. 1 IntroductionIn most of modern public security markets, the price formation process, or price discovery, results from competition between several market agents that take part in a public auction. In particular, day trading sessions, which are also called continuous trading phases, consist of continuous double auctions. In these situations, liquidity providers 1 continuously set bid and ask prices for the considered security, and the marketplace publicly displays a (possibly partial) information about these bid and ask prices, along with transactions prices. The action of continuously providing bid and ask quotes during day trading sessions is called market making, and this role was tradionnally performed by specialist firms. However, due to the recent increased availability of electronic trading technologies, as well as regulatory changes, a large range of investors are now able to implement such market making strategies. These strategies are part of the broader category of high frequency trading (HFT) strategies, which are characterized by the fact that they facilitate a larger number of orders being sent to the market per unit of time. HFT takes place in the continuous trading phase, and ...

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“…where X k ∈ {1, 2, ..., n} := X is a continuous-time n-state Markov chain, a(x) is continuous and bounded function on X = {1, 2, ..., n}, N (t) is the non-linear Hawkes process (see, e.g., [46]) defined by the intensity function in the following form (see (9), Definition 6):…”

Section: Diffusion Limits and Llns For Non-linear Compound Hawkes Promentioning

confidence: 99%

“…Cartea et al (2011) [9] applied HP to model market order arrivals. Filimonov and Sornette (2012) [25] and Filimonov et al (2013) [26] apply the HP to estimate the persentage of price changes caused by endogeneous self-generated activity rather than the exogeneous impact of news or novel information.…”

Section: Introductionmentioning

confidence: 99%

General Compound Hawkes Processes in Limit Order Books

Swishchuk

2017

SSRN Journal

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Abstract:In this paper, we further study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) for these processes. The latter two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by studying the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes.

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Buy Low, Sell High: A High Frequency Trading Perspective

Cited by 132 publications

References 17 publications

Optimal Placement in a Limit Order Book

Optimal Placement in a Limit Order Book

Optimal High‐frequency Trading in a Pro Rata Microstructure With Predictive Information

General Compound Hawkes Processes in Limit Order Books

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