An ephemerally self-exciting point process

Daw, Andrew; Pender, Jamol

doi:10.1017/apr.2021.35

Cited by 12 publications

(31 citation statements)

References 63 publications

(91 reference statements)

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“…In this section, the Q-Hawkes process is discussed, expanding on the analytical properties derived in [5]. Specifically, we show that the intensity of the Q-Hawkes process admits a closed-form probability mass function (PMF), and that the characteristic function of the compensated jump term M t (see Equation ( 7)) has an analytical solution.…”

Section: The Heston-queue-hawkes Modelmentioning

confidence: 90%

“…The Q-Hawkes process was recently introduced in [5] as a possible alternative to the Hawkes process. Instead of being determined by a counting process and a time-dependent memory kernel, the Q-Hawkes process consists of two counting processses (N t and N Q t ).…”

Section: The Q-hawkes Processmentioning

confidence: 99%

“…In spite of this, the Hawkes process has remained the model of choice for contagion, and many variants of the original process have emerged to cope with more specific and complex phenomena. It is in this context that an alternative to the Hawkes process with fully analytical characteristic function was recently introduced in [5]. The process there developed, the so-called Queue-Hawkes (Q-Hawkes) process-a particular type ephemerally self-exciting (ESE) process-enjoys similar properties to the Hawkes process, such as self-excitation and reversion to the base level.…”

Section: Introductionmentioning

confidence: 99%

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A new self-exciting jump-diffusion process for option pricing

Arias¹,

Cirillo²,

Oosterlee³

2022

Preprint

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We propose a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion. However, since the characteristic function of the HQH process is known in closed-form, Fourier-based fast pricing algorithms, like the COS method, can be fully exploited with this model. Furthermore, we show that by using partial integrals of the characteristic function, which are also explicitly known for the HQH process, we can reduce the dimensionality of the COS method, and so its numerical complexity. Numerical results for European and Bermudan options show that the HQH model offers a wider range of volatility smiles compared to the Bates model, while its computational burden is considerably smaller than that of the Heston-Hawkes (HH) process.

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Section: The Heston-queue-hawkes Modelmentioning

confidence: 90%

Section: The Q-hawkes Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new self-exciting jump-diffusion process for option pricing

Arias¹,

Cirillo²,

Oosterlee³

2022

Preprint

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“…Embrechts and Kirchner (2018) propose several graph-theoretic objects which summarize the branching structure of a multivariate Hawkes process. Daw and Pender (2018a) propose an ephemerally self-excited process which adds an additional stochastic component to the time in which excitement affects the process. Intuitively, this is motivated by how past events in epidemics only influence the future as long as the event stays active (say, as long as a person is infectious).…”

Section: Other Modeling Paradigms and Their Links To The Hawkes Modelmentioning

confidence: 99%

Interval-censored Hawkes processes

Rizoiu

Soen

et al. 2021

Preprint

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Hawkes processes are a popular means of modeling the event times of self-exciting phenomena, such as earthquake strikes or tweets on a topical subject. Classically, these models are fit to historical event time data via likelihood maximization. However, in many scenarios, the exact times of historical events are not recorded for either privacy (e.g., patient admittance to hospitals) or technical limitations (e.g., most transport data records the volume of vehicles passing loop detectors but not the individual times). The interval-censored setting denotes when only the aggregate counts of events at specific time intervals are observed. Fitting the parameters of interval-censored Hawkes processes requires designing new training objectives that do not rely on the exact event times.In this paper, we propose a model to estimate the parameters of a Hawkes process in interval-censored settings. Our model builds upon the existing Hawkes Intensity Process (HIP) of Rizoiu et al. (2017b) in several important directions. First, we observe that while HIP is formulated in terms of expected intensities, it is more natural to work instead with expected counts; further, one can express the latter as the solution to an integral equation closely related to the defining equation of HIP. Second, we show how a non-homogeneous Poisson approximation to the Hawkes process admits a tractable likelihood in the intervalcensored setting; this approximation recovers the original HIP objective as a special case, and allows for the use of a broader class of Bregman divergences as loss function. Third, we explicate how to compute a tighter approximation to the ground truth in the likelihood. Finally, we show how our model can incorporate information about varying interval lengths. Experiments on synthetic and real-world data confirm our HIPPer model outperforms HIP and several other baselines on the task of interval-censored inference.

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“…This method can be also applied for other Markov process whose moments are easy to compute by exploiting the structure of a new sequence of nested matrices called Matryoshkhan matrices; see [9] for details. One can work with generalization of the Hawkes process as well called the ephemerally self-exciting process; see [10]. The connection of the Hawkes process with social media has not been yet understood well though, in our opinion.…”

Section: Introductionmentioning

confidence: 99%

Modeling social media contagion using Hawkes processes

Palmowski¹,

Puchalska²

2020

Preprint

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The contagion dynamics can emerge in social networks when repeated activation is allowed. An interesting example of this phenomenon is retweet cascades where users allow to re-share content posted by other people with public accounts. To model this type of behaviour we use a Hawkes self-exciting process. To do it properly though one needs to calibrate model under consideration. The main goal of this paper is to construct moments method of estimation of this model. The key step is based on identifying of a generator of a Hawkes process. We perform numerical analysis on real data as well.

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An ephemerally self-exciting point process

Cited by 12 publications

References 63 publications

A new self-exciting jump-diffusion process for option pricing

A new self-exciting jump-diffusion process for option pricing

Interval-censored Hawkes processes

Modeling social media contagion using Hawkes processes

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