Hawkes processes and some financial applications

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dc.contributor.advisorMacDonald, Iain Len_ZA
dc.contributor.authorLapham, Brendon Men_ZA
dc.date.accessioned2014-10-17T10:09:51Z
dc.date.available2014-10-17T10:09:51Z
dc.date.issued2014en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractThe self-exciting point process, which is now more commonly known as the Hawkes process, is a model for a point process on the real line introduced by Hawkes (1971). The distinguishing feature of such processes is that they allow all past `events' to affect the intensity function at the current time. Over the years such processes have been applied in seismology and neurophysiology in particular, and in more recent years there have been significant financial applications. In almost all of these applications, the route used to find the maximum likelihood estimates (MLEs) is direct numerical maximisation (DNM) of the likelihood. An EM algorithm, which makes use of the Poisson cluster process interpretation of the Hawkes process, is an alternative route to the MLEs. This particular EM algorithm has received attention in the literature and has been claimed to have advantages over DNM of the likelihood. We carry out a simulation study for a simple Hawkes process to clarify statements made in the literature about these advantages. For the simple Hawkes process models that we consider, DNM of the likelihood is the preferable route to finding the MLEs. We then use DNM of the likelihood to _t marked Hawkes process models to South African asset data. These applications to South African data include the modelling of extreme asset returns and the forecasting of conditional value-at-risk (VaR) and expected shortfall (ES). The models investigated include mostly models found in the literature, but also include some variations introduced here. In a backtesting exercise, we compare the conditional VaR and ES forecasts found by using the marked Hawkes process models with those found via some nonstandard stochastic volatility (SV) models. We find that the marked Hawkes process models give mostly competitive forecasts of conditional VaR and ES when compared with the nonstandard SV models.en_ZA
dc.identifier.apacitationLapham, B. M. (2014). <i>Hawkes processes and some financial applications</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/8523en_ZA
dc.identifier.chicagocitationLapham, Brendon M. <i>"Hawkes processes and some financial applications."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014. http://hdl.handle.net/11427/8523en_ZA
dc.identifier.citationLapham, B. 2014. Hawkes processes and some financial applications. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Lapham, Brendon M AB - The self-exciting point process, which is now more commonly known as the Hawkes process, is a model for a point process on the real line introduced by Hawkes (1971). The distinguishing feature of such processes is that they allow all past `events' to affect the intensity function at the current time. Over the years such processes have been applied in seismology and neurophysiology in particular, and in more recent years there have been significant financial applications. In almost all of these applications, the route used to find the maximum likelihood estimates (MLEs) is direct numerical maximisation (DNM) of the likelihood. An EM algorithm, which makes use of the Poisson cluster process interpretation of the Hawkes process, is an alternative route to the MLEs. This particular EM algorithm has received attention in the literature and has been claimed to have advantages over DNM of the likelihood. We carry out a simulation study for a simple Hawkes process to clarify statements made in the literature about these advantages. For the simple Hawkes process models that we consider, DNM of the likelihood is the preferable route to finding the MLEs. We then use DNM of the likelihood to _t marked Hawkes process models to South African asset data. These applications to South African data include the modelling of extreme asset returns and the forecasting of conditional value-at-risk (VaR) and expected shortfall (ES). The models investigated include mostly models found in the literature, but also include some variations introduced here. In a backtesting exercise, we compare the conditional VaR and ES forecasts found by using the marked Hawkes process models with those found via some nonstandard stochastic volatility (SV) models. We find that the marked Hawkes process models give mostly competitive forecasts of conditional VaR and ES when compared with the nonstandard SV models. DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - Hawkes processes and some financial applications TI - Hawkes processes and some financial applications UR - http://hdl.handle.net/11427/8523 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/8523
dc.identifier.vancouvercitationLapham BM. Hawkes processes and some financial applications. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/8523en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.titleHawkes processes and some financial applicationsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMBusScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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