Meerschaert, Mark M and Scalas, Enrico (2006) Coupled continuous time random walks in finance. Physica A: Statistical Mechanics and its Applications, 370 (1). pp. 114-118. ISSN 0378-4371

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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.

Item Type:	Article
Schools and Departments:	School of Mathematical and Physical Sciences > Mathematics
Subjects:	Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User:	Enrico Scalas
Date Deposited:	30 Sep 2014 13:56
Last Modified:	30 Sep 2014 13:56
URI:	http://sro.sussex.ac.uk/id/eprint/50277

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