On Lewis' simulation method for point processes

We present a Hawkes model approach to foreign exchange market in which the high frequency price dynamics is affected by a self exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By focusing on time windows around the news announcement, we find that the model is able to capture the increase of trading activity after the news, both when the news has a sizeable effect on volatility and when this effect is negligible, either because the news in not important or because the announcement is in line with the forecast by analysts. We extend the model by considering non-causal effects, due to the fact that the existence of the news (but not its content) is known by the market before the announcement.

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“…Ogata [34] shown that the log likelihood can be computed recursively reducing computational complexity to O(N).…”

Section: Discussionmentioning

confidence: 99%

Modeling foreign exchange market activity around macroeconomic news: Hawkes-process approach

2015

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“…This is demonstrated in the example in Figure 2.1 below. This simulation, in addition to all the others throughout this work, is constructed by use of the algorithm described in Ogata [21]. , β = 1, and λ * = 1.…”

Section: Comparison To the Poisson Processmentioning

confidence: 99%

“…In each example we derive the simulated functions via 100,000 replications of the procedure described in Ogata [21]. We start with the mean and variance of a single phase system, as shown in the pair of plots below in Figure 3 , λ * = µ = 1.…”

Section: Simulation Studymentioning

confidence: 99%

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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“…Note also that simulation algorithms of Hawkes processes are easily available (see e.g. Ogata, 1981;Moller and Rasmussen, 2005, and Appendix A), allowing further developments for the use of the estimated models. These practical properties make Hawkes processes good candidates for the study of the clustering of events empirically observed in order book models (Hautsch, 2004;Bowsher, 2007;Large, 2007;Bacry et al, 2012).…”

Section: Testing the Calibrationmentioning

confidence: 99%

“…Appendix A -Simulation of Hawkes processes Ogata (1981) proposes an algorithm for the simulation of Hawkes processes, based on a general procedure called thinning. Taking a different point of view, a more recent work by Moller and Rasmussen (2005) claims to provide better quality simulations, without edge effects.…”

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confidence: 99%