The Price Impact of Order Book Events

Cont, Rama; Kukanov, Arseniy; Stoikov, Sasha

doi:10.2139/ssrn.1712822

Cited by 48 publications

(22 citation statements)

References 60 publications

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“…Recent empirical studies of the dependency of price change on the imbalance of the order book (see [5,22]) suggest linear behaviour for balanced order books and non-linear behaviour when imbalance is large. • In addition to mild and weak solutions as in [19] we obtain solutions in the analytically strong sense and make the transformation from free to fixed boundary, that is introduced in a deterministic setting in [24] and used in [19], rigorous in a stochastic setting.…”

Section: Introductionmentioning

confidence: 99%

A Stefan-type stochastic moving boundary problem

Keller‐Ressel

Müller

2016

Stoch PDE: Anal Comp

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Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform the problem from a moving boundary problem into a stochastic evolution equation with fixed boundary conditions. Using results from interpolation theory we obtain existence and uniqueness of local strong solutions, extending results of Kim, Zheng and Sowers. In addition, we formulate conditions for existence of global solutions and provide a refined analysis of possible blow-up behavior in finite time.Comment: 34 page

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Section: Introductionmentioning

confidence: 99%

A Stefan-type stochastic moving boundary problem

Keller‐Ressel

Müller

2016

Stoch PDE: Anal Comp

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“…Among the various approaches, the researchers agree on the intuitive notion that "imbalance between supply and demand moves prices" [5]. That is, when there are many more shares available at the ask price than the bid price, or vice versa, there is pressure on the price to change.…”

Section: Literature Reviewmentioning

confidence: 99%

“…That is, when there are many more shares available at the ask price than the bid price, or vice versa, there is pressure on the price to change. Cont et al drew from economic theory in modeling order flow imbalance (OFI) as the imbalance in supply and demand caused by an order book event, and proposed a simple linear relationship between OFI and price change [5]. The OFI is a running total of the net order flow at the National Best Bid and Offer (NBBO) and is defined as:…”

Section: Literature Reviewmentioning

confidence: 99%

“…Increasing every time the bid size increases, the ask size decreases or the bid/ask prices increase 2. Decreases every time the bid size decreases, the ask size increases or the bid/ask prices decrease [5] This definition leads to a strikingly simple model of one variable, as the OFI incorporates several market factors into a singular quantitative measure. It is not even necessary to distinguish between the OFI changing as a result of orders being filled or canceled, just that the bid/ask prices and sizes change [6].…”

Section: Literature Reviewmentioning

confidence: 99%

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Effect of order flow imbalance on market impact across market states

Kromkowski

Montgomery

Saha

et al. 2016

2016 IEEE Systems and Information Engineering Design Symposium (SIEDS)

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Every time a trader places an order to buy or sell a stock, this order causes reactions that change the market in highly complex ways. In theory these changes are always detrimental to the trader, causing the stock to become more expensive when buying and cheaper when selling. For large hedge funds, these costs have the potential to become a major obstruction to profitability when aggregated. Market impact models have been based on simple supply and demand, no arbitrage theory, and Brownian motion. These previous models have shown that the market impact of orders and trades can be largely explained using a linear model with Order Flow Imbalance (OFI), a simple measure of the buy/sell imbalance of quote orders placed to the National Best Bid and Offer (NBBO) in a window of time, as the sole predictor. By examining this relationship between OFI and price movement, previous studies have derived observable measures for the market impact of orders placed in a period of time, however these models are unsurprisingly noisy. Using a simple Brownian motion model for the movement of prices, we propose a new method for observing this price impact and compare it to previously accepted models. We then use this measure to examine how price impact varies across market states (i.e. volume, time of day, and spread).

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“…movements larger than 1% in one tick). A more sophisticated pre-cleaning procedure for TAQ data can be found in Barndorff-Nielsen et al (2009) and Cont et al (2013). An example of cleaned data is illustrated in figure 4.…”

Section: Data Preparationmentioning

confidence: 99%

Evolution of high-frequency systematic trading: a performance-driven gradient boosting model

Zhou¹,

Cheng²,

Qin

et al. 2015

Quantitative Finance

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This paper proposes a performance-driven gradient boosting model (pdGBM) which predicts shorthorizon price movements by combining nonlinear response functions of selected predictors. This model performs gradient descent in a constrained functional space by directly minimizing loss functions customized with different trading performance measurements. To demonstrate its practical applications, a simple trading system was designed with trading signals constructed from pdGBM predictions and fixed holding period in each trade. We tested this trading system on the highfrequency data of SPDR S&P 500 index ETF (SPY). In the out-of-sample period, it generated an average of 0.045% return per trade and an annualized Sharpe ratio close to 20 after transaction costs. Various empirical results also showed the model robustness to different parameters. These superior performances confirm the predictability of short-horizon price movements in the US equity market. We also compared the performance of this trading system with similar trading systems based on other predictive models like the gradient boosting model with L2 loss function and the penalized linear model. Results showed that pdGBM substantially outperformed all other models by higher returns in each month of the testing period. Additionally, pdGBM has many advantages including its capability of automatic predictor selection and nonlinear pattern recognition, as well as its simply structured and interpretable output function.

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The Price Impact of Order Book Events

Cited by 48 publications

References 60 publications

A Stefan-type stochastic moving boundary problem

A Stefan-type stochastic moving boundary problem

Effect of order flow imbalance on market impact across market states

Evolution of high-frequency systematic trading: a performance-driven gradient boosting model

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