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Modelling microstructure noise with mutually exciting point processes

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BDHM1.pdf (386.2Kb)
Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00779787
Dewey
Probabilités et mathématiques appliquées
Sujet
Epps effect; Signature plot; Bartlett spectrum; Hawkes processes; Point processes; Microstructure noise
Journal issue
Quantitative Finance
Volume
13
Number
1
Publication date
2013
Article pages
65-77
Publisher
Institute of Physics Publishing
DOI
http://dx.doi.org/10.1080/14697688.2011.647054
URI
https://basepub.dauphine.fr/handle/123456789/10890
Collections
  • CEREMADE : Publications
Metadata
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Author
Muzy, Jean-François
Hoffmann, Marc
Delattre, Sylvain
Bacry, Emmanuel
Type
Article accepté pour publication ou publié
Abstract (EN)
We 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.

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