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Modelling microstructure noise with mutually exciting point processes

dc.contributor.authorMuzy, Jean-François
HAL ID: 8572
dc.contributor.authorHoffmann, Marc
dc.contributor.authorDelattre, Sylvain
dc.contributor.authorBacry, Emmanuel
HAL ID: 735850
ORCID: 0000-0001-5997-1942
dc.date.accessioned2013-01-26T10:54:20Z
dc.date.available2013-01-26T10:54:20Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10890
dc.language.isoenen
dc.subjectEpps effecten
dc.subjectSignature ploten
dc.subjectBartlett spectrumen
dc.subjectHawkes processesen
dc.subjectPoint processesen
dc.subjectMicrostructure noiseen
dc.subject.ddc519en
dc.titleModelling microstructure noise with mutually exciting point processesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point pro- cesses and relies on linear self and mutually exciting stochastic inten- sities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.en
dc.relation.isversionofjnlnameQuantitative Finance
dc.relation.isversionofjnlvol13en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages65-77en
dc.relation.isversionofdoihttp://dx.doi.org/10.1080/14697688.2011.647054en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00779787en
dc.relation.isversionofjnlpublisherInstitute of Physics Publishingen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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