Hawkes Process: Fast Calibration, Application to Trade Clustering and Diffusive Limit

Fonseca, José Da; Zaatour, Riadh

doi:10.2139/ssrn.2294112

Cited by 70 publications

(116 citation statements)

References 45 publications

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“…These results can be found in greater detail in Dassios and Zhao [5], Da Fonseca and Zaatour [3,4], as discussed specifically after each result statement. This review is primarily focused on the transient and stationary moments of the Hawkes process, and is included both for the sake of completeness and understanding of the problem, but also so that it may be incorporated later in this work.…”

Section: Review Of Relevant Hawkes Process Literaturementioning

confidence: 71%

“…If one applies Ito's lemma to the kernel function e −βt λ t , then one can show that 5) as in [3], which also discusses the impact of the initial value of the intensity λ 0 . This process is known to be stable for α < β, see [12].…”

Section: Hawkes Arrival Processmentioning

confidence: 99%

“…This follows directly from the approach involving the infinitesimal generator described in Sections 2.1 and 2.2 of [3], followed by simplification using the binomial theorem. For the first and second moments of N t and λ t and the first product moment, these equations are stated exactly in that work.…”

Section: Review Of Relevant Hawkes Process Literaturementioning

confidence: 99%

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Queues Driven by Hawkes Processes

Daw

Pender

2017

SSRN Journal

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Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through selfexcitation of the arrival process. In this paper, we analyze an infinite server queueing system in which the arrivals are driven by the self-exciting Hawkes process and where service follows a phase-type distribution or is deterministic. In the phase-type setting, we derive differential equations for the moments and a partial differential equation for the moment generating function; we also derive exact expressions for the transient and steady-state mean, variance, and covariances. Furthermore, we also derive exact expressions for the auto-covariance of the queue and provide an expression for the cumulant moment generating function in terms of a single ordinary differential equation. In the deterministic service setting, we provide exact expressions for the first and second moments and the queue auto-covariance. As motivation for our Hawkes queueing model, we demonstrate its usefulness through two novel applications. These applications are trending internet traffic and arrivals to nightclubs. In the web traffic setting, we investigate the impact of a click. In the nightclub or Club Queue setting, we design an optimal control problem for the optimal rate to admit club-goers.

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Section: Review Of Relevant Hawkes Process Literaturementioning

confidence: 71%

Section: Hawkes Arrival Processmentioning

confidence: 99%

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Queues Driven by Hawkes Processes

Daw

Pender

2017

SSRN Journal

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“…With respect to the clustering and mean reversion effect, this model generalizes the pioneer work of Bacry et al () which considers only the mean reversion effect. It also generalizes the work of Da Fonseca and Zaatour (), which considers only the clustering effect. As this general model encompasses both of the previously developed models, it is of interest to determine whether the phenomena are really needed.…”

Section: Applicationsmentioning

confidence: 67%

Clustering and Mean Reversion in a Hawkes Microstructure Model

Fonseca

Zaatour

2014

Journal of Futures Markets

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This paper provides explicit formulas for the first and second moments and the autocorrelation function of the number of jumps over a given interval for the multivariate Hawkes process. These computations are possible thanks to the affine property of this process. We unify the stock price models of Bacry et al. (2013a, Quantitative Finance, 13, 65–77) and Da Fonseca and Zaatour (2014, Journal of Futures Markets) both of them based on the Hawkes process, the first one having a mean reverting behavior while the second one a clustering behavior, and build a model having these two properties. We compute various statistics as well as the diffusive limit for the stock price that determines the connection between the parameters driving the high‐frequency activity to the daily volatility. Lastly, the impulse function giving the impact on the stock price of a buy/sell trade is explicitly computed. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:813–838, 2015

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“…Both informed trading and liquidity trading tend to concentrate whenever the market is active with abundant available orders, so as to minimize the liquidity impact on prices and to benefit from short-lived information as much as possible before its widespread dissemination (Admati & Pfleiderer, 1988;Da Fonseca & Zaatour, 2014, 2015Sarkar & Schwartz, 2006). Both informed trading and liquidity trading tend to concentrate whenever the market is active with abundant available orders, so as to minimize the liquidity impact on prices and to benefit from short-lived information as much as possible before its widespread dissemination (Admati & Pfleiderer, 1988;Da Fonseca & Zaatour, 2014, 2015Sarkar & Schwartz, 2006).…”

Section: Institutional Individual and High-frequency Tradingmentioning

confidence: 99%

Institutional high frequency trading and price discovery: Evidence from an emerging commodity futures market

Zhao

Di-fang

2017

Journal of Futures Markets

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We compare the effects of institutional and individual trading on intraday price processes in the emerging commodity futures market of China with a unique trade‐by‐trade dataset. Institutional investors collectively facilitate price discovery with positive permanent price impacts, but their beneficial role is time agglomerated, that is, only institutional highly‐concentrated trades executed at the same millisecond are accompanied by information effects. Transitory price disturbances are mitigated by informed institutional highly‐concentrated trading in the agricultural sector, whereas these disturbances are alleviated by liquidity‐enhancing individual trading in the industrial sector. Overall, the entire market is abnormally dominated by transitory volatility instead of informational volatility.

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Hawkes Process: Fast Calibration, Application to Trade Clustering and Diffusive Limit

Cited by 70 publications

References 45 publications

Queues Driven by Hawkes Processes

Queues Driven by Hawkes Processes

Clustering and Mean Reversion in a Hawkes Microstructure Model

Institutional high frequency trading and price discovery: Evidence from an emerging commodity futures market

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