Coupled continuous time random walks in finance

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dc.creatorMeerschaert, Mark M.
dc.creatorScalas, Enrico
dc.date2006-08-29
dc.date.accessioned2026-07-07T12:11:27Z
dc.date.available2026-07-07T12:11:27Z
dc.descriptionContinuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that generalize the familiar stable models. In this paper, we will review the fundamental theory and present two applications with tick-by-tick stock and futures data.
dc.description7 pages, 2 figures. Paper presented at the Econophysics Colloquium, Canberra, Australia, November 2005
dc.identifierhttps://arxiv.org/abs/physics/0608281
dc.identifierhttp://arxiv.org/abs/physics/0608281
dc.identifierPhysica A, vol. 370, 114-118, 2006
dc.identifierdoi:10.1016/j.physa.2006.04.034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210226
dc.subjectData Analysis, Statistics and Probability
dc.subjectPhysics and Society
dc.subjectStatistical Finance
dc.titleCoupled continuous time random walks in finance
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