Hawkes Processes and Their Applications to High‐Frequency Data Modeling

Law, Baron; Viens, Frederi

doi:10.1002/9781118593486.ch7

Cited by 9 publications

(9 citation statements)

References 71 publications

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“…Together with the buy and sell market order

M_{t}^{+}, M_{t}^{-}

, the quadruplet

(N_{t}^{+}, N_{t}^{-}, M_{t}^{+}, M_{t}^{-})

forms a multivariate Hawkes process (Hawkes, 1971a, 1971b; Law & Viens, ).…”

Section: Consistency Of Limit Order Book Modelmentioning

confidence: 99%

“…Together with the buy and sell market order M + t , M − t , the quadruplet (N + t , N − t , M + t , M − t ) forms a multivariate Hawkes process [19][20][21].…”

Section: Examples Of Inconsistent Modelsmentioning

confidence: 99%

“…However, including Q a t in the model would significantly increase the dimension of the state variables needed for modeling, as we need to keep track of the order flow at all price levels, not just the best bid/ask [25] 19 . Moreover, the practices of quote stuffing 20 [26] and spoofing 21 [27] render the usefulness of the full LOB questionable, especially beyond the best quotes. As a result, the benefit of a full LOB model may not justify the added nontrivial complexity and this may explain the emergence of reduced-form models, which focus only on the top of the book [28,29].…”

Section: Intensity and Mark Distributionsmentioning

confidence: 99%

“…For example, we need to keep track of orders falling at the second best, otherwise we would have no way to compute the queue depth of the new best quote after an aggressive market order 20. Rapid placement and cancellation of large amount of limit orders 21. Submission of limit orders to create an illusion of demand/supply imbalance 22.…”

mentioning

confidence: 99%

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Market making under a weakly consistent limit order book model

Law¹,

Viens

2019

High Frequency

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We develop a new market‐making model, from the ground up, which is tailored toward high‐frequency trading under a limit order book (LOB), based on the well‐known classification of order types in market microstructure. Our flexible framework allows arbitrary order volume, price jump, and bid‐ask spread distributions as well as the use of market orders. It also honors the consistency of price movements upon arrivals of different order types. For example, it is apparent that prices should never go down on buy market orders. In addition, it respects the price‐time priority of LOB. In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov (Quantitative Finance, 8, 217, 2008) market‐making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order book features. The Hamilton‐Jacobi‐Bellman quasi‐variational inequality (HJBQVI) associated with the control problem can be solved numerically via finite‐difference method. We illustrate our optimal trading strategy with a full numerical analysis, calibrated to the order book statistics of a popular exchanged‐traded fund (ETF). Our simulation shows that the profit of market‐making can be severely overstated under LOBs with inconsistent price movements.

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“…Together with the buy and sell market order

M_{t}^{+}, M_{t}^{-}

, the quadruplet

(N_{t}^{+}, N_{t}^{-}, M_{t}^{+}, M_{t}^{-})

forms a multivariate Hawkes process (Hawkes, 1971a, 1971b; Law & Viens, ).…”

Section: Consistency Of Limit Order Book Modelmentioning

confidence: 99%

“…Together with the buy and sell market order M + t , M − t , the quadruplet (N + t , N − t , M + t , M − t ) forms a multivariate Hawkes process [19][20][21].…”

Section: Examples Of Inconsistent Modelsmentioning

confidence: 99%

Section: Intensity and Mark Distributionsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Market making under a weakly consistent limit order book model

Law¹,

Viens

2019

High Frequency

Self Cite

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show abstract

“…Since then, the model has often been applied to financial data. Bacry et al (2015), Law and Viens (2015), and Hawkes (2018) summarize recent developments in the application of the Hawkes process to finance.…”

Section: Introductionmentioning

confidence: 99%

Modeling bid and ask price dynamics with an extended Hawkes process and its empirical applications for high-frequency stock market data

Lee,

Seo

2022

Preprint

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This study proposes a versatile model for the dynamics of the best bid and ask prices using an extended Hawkes process. The model incorporates the zero intensities of the spreadnarrowing processes at the minimum bid-ask spread, spread-dependent intensities, possible negative excitement, and nonnegative intensities. We apply the model to high-frequency best bid and ask price data from US stock markets. The empirical findings demonstrate a spread-narrowing tendency, excitations of the intensities caused by previous events, the impact of flash crashes, characteristic trends in fast trading over time, and the different features of market participants in the various exchanges.

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Simulating Fake News Dissemination on Twitter with Multivariate Hawkes Processes

Jiang

Porter

2022

2022 IEEE International Conference on Big Data (Big Data)

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Fake news has emerged as a pervasive problem within Online Social Networks, leading to a surge of research interest in this area. Understanding the dissemination mechanisms of fake news is crucial in comprehending the propagation of disinformation/misinformation and its impact on users in Online Social Networks. This knowledge can facilitate the development of interventions to curtail the spread of false information and inform affected users to remain vigilant against fraudulent/malicious content. In this paper, we specifically target the Twitter platform and propose a Multivariate Hawkes Point Processes model that incorporates essential factors such as user networks, response tweet types, and user stances as model parameters. Our objective is to investigate and quantify their influence on the dissemination process of fake news. We derive parameter estimation expressions using an Expectation Maximization algorithm and validate them on a simulated dataset. Furthermore, we conduct a case study using a real dataset of fake news collected from Twitter to explore the impact of user stances and tweet types on dissemination patterns. This analysis provides valuable insights into how users are influenced by or influence the dissemination process of disinformation/misinformation, and demonstrates how our model can aid in intervening in this process.

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Hawkes Processes and Their Applications to High‐Frequency Data Modeling

Cited by 9 publications

References 71 publications

Market making under a weakly consistent limit order book model

Market making under a weakly consistent limit order book model

Modeling bid and ask price dynamics with an extended Hawkes process and its empirical applications for high-frequency stock market data

Simulating Fake News Dissemination on Twitter with Multivariate Hawkes Processes

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