Coupled continuous time random walks in finance

Mark M. Meerschaert and Enrico Scalas

Physica A: Statistical Mechanics and its Applications, 2006, vol. 370, issue 1, 114-118

Abstract: Continuous 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.

Keywords: Anomalous diffusion; Continuous time random walks; Heavy tails; Fractional calculus (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:370:y:2006:i:1:p:114-118

DOI: 10.1016/j.physa.2006.04.034

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