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Scaling properties and universality of first-passage-time probabilities in financial markets

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Perelló, Josep, Gutiérrez-Roig, Mario and Masoliver, Jaume (2011) Scaling properties and universality of first-passage-time probabilities in financial markets. Physical Review E, 84 (6). 066110 . doi:10.1103/PhysRevE.84.066110 ISSN 1539-3755.

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Official URL: http://dx.doi.org/10.1103/PhysRevE.84.066110

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Abstract

Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics, mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered, resulting in fat-tailed first-passage time probabilities. The scaling of the return with its standard deviation collapses the probabilities of all markets examined—and also for different time horizons—into single curves, suggesting that first-passage statistics is market independent (at least for high-frequency data). On the other hand, a very closely related quantity, the survival probability, shows, away from the center and tails of the distribution, a hyperbolic
t
−
1
/
2
decay typical of a Markovian dynamics, albeit the existence of memory in markets. Modifications of the Weibull and Student distributions are good candidates for the phenomenological description of first-passage time properties under certain regimes. The scaling strategies shown may be useful for risk control and algorithmic trading.

Item Type: Journal Article
Divisions: Faculty of Social Sciences > Warwick Business School > Behavioural Science
Faculty of Social Sciences > Warwick Business School
Journal or Publication Title: Physical Review E
Publisher: American Physical Society
ISSN: 1539-3755
Official Date: 14 December 2011
Dates:
DateEvent
14 December 2011Published
Volume: 84
Number: 6
Article Number: 066110
DOI: 10.1103/PhysRevE.84.066110
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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