Buy Low Sell High: A High Frequency Trading Perspective

Cartea, Álvaro; Jaimungal, Sebastian; Ricci, Jason

doi:10.2139/ssrn.1964781

Cited by 89 publications

(130 citation statements)

References 24 publications

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“…The model in [8,40] has been further complemented by explicitly accounting for inventory constraints [15,33]. More sophisticated models have also been proposed including for example richer dynamics of market orders, impact on the limit order book, adverse selection effects and pre- dictability, to deal with high frequency market making [17]. Further generalizations include market orders and limit orders at best as well as next to best bid and ask together with stochastic spreads [36].…”

Section: High Frequency Tradingmentioning

confidence: 99%

“…Such models can be devised and to some extent calibrated, see [17] in particular, but by accounting for all these aspects analytic tractability is easily lost and one has to rely either on first order approximations or on numerical approximations for the associated partial differential equations. In this paper our focus is on the market making problem, as well as the problem of optimal portfolio liquidation using limit orders, and a distinct feature of our paper is that we consider these problems under model risk or uncertainty.…”

Section: Modelmentioning

confidence: 99%

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Market Making and Portfolio Liquidation Under Uncertainty

Nyström

Aly

Zhang

2014

Int. J. Theor. Appl. Finan.

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Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

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Section: High Frequency Tradingmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Market Making and Portfolio Liquidation Under Uncertainty

Nyström

Aly

Zhang

2014

Int. J. Theor. Appl. Finan.

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“…This question of determining the optimal price level is often called the optimal placement problem of a limit order. In Cartea, Jaimungal, and Ricci (), a problem of market‐making is studied under a diffusion model for the midprice with constant volatility and a stochastic mean‐reverting drift process with jumps. More specifically, it is assumed therein that the trader is continuously posting and canceling LOs to maximize the expected terminal wealth while penalizing unfilled total inventory during the specified trading period.…”

Section: Introductionmentioning

confidence: 99%

Optimal placement of a small order in a diffusive limit order book

2018

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We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, using a limit order or a market order. For a diffusive market, we characterize the optimal limit order placement policy and analyze its behavior under different market conditions. In particular, we show that, in the presence of a negative drift, there exists a critical time t0 > 0 such that, for any time horizon t > t0, there exists an optimal placement, which, contrary to earlier work, is different from one that is placed “infinitesimally” close to the best ask, such as the best bid and second best bid. We also propose a simple method to approximate the critical time t0 and the optimal order placement.

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“…For instance, among the trading transactions of US in 2012, high-frequency trading accounted for 84% in stock trades and 51% in equity value (Popper 2012). Clearly, the characteristics of order-driven trading systems change the dynamics of the markets and demand new trading strategies that can capture short-term behaviour of underlying assets (Parlour 1998, Foucault 1999, Bovier et al 2006, Cartea et al 2014.…”

Section: Introductionmentioning

confidence: 99%

Modelling high-frequency limit order book dynamics with support vector machines

Kercheval

Zhang

2015

Quantitative Finance

118

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We propose a machine learning framework to capture the dynamics of high-frequency limit order books in financial equity markets and automate real-time prediction of metrics such as mid-price movement and price spread crossing. By characterizing each entry in a limit order book with a vector of attributes such as price and volume at different levels, the proposed framework builds a learning model for each metric with the help of multi-class support vector machines. Experiments with real data establish that features selected by the proposed framework are effective for short-term price movement forecasts.

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Buy Low Sell High: A High Frequency Trading Perspective

Cited by 89 publications

References 24 publications

Market Making and Portfolio Liquidation Under Uncertainty

Market Making and Portfolio Liquidation Under Uncertainty

Optimal placement of a small order in a diffusive limit order book

Modelling high-frequency limit order book dynamics with support vector machines

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