Coupled continuous time random walks in finance

By Mark M. Meerschaert, Enrico Scalas. 2006

207 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5d44fe1ec8b32c4c7366e86105b566a75ea41661

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Citations in the corpus

TEMPERED FRACTIONAL CALCULUS (2015, background): “They are now used to model a wide variety of problems in physics [24, 35,38,50,51,55,65], finance [23,27,37,42,60,61], biology [2,4,22,26,36], and hydrology [1,7,8,15,17,62].”
Triangular array limits for continuous time random walks (2008, background): “Continuous time random walks and the associated fractional diffusion equations are useful in physics [42,43], finance [23,33,41,47,48,52], and hydrology [10,12,55].”