dorsal/arxiv
View SchemaCoupled continuous time random walks in finance
| Authors | Mark M. Meerschaert, Enrico Scalas |
|---|---|
| Categories | |
| ArXiv ID | physics/0608281 |
| URL | https://arxiv.org/abs/physics/0608281 |
| DOI | 10.1016/j.physa.2006.04.034 |
| Journal | Physica A, vol. 370, 114-118, 2006 |
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.
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"abstract": "Continuous time random walks (CTRWs) are used in physics to model anomalous\ndiffusion, by incorporating a random waiting time between particle jumps. In\nfinance, the particle jumps are log-returns and the waiting times measure delay\nbetween transactions. These two random variables (log-return and waiting time)\nare typically not independent. For these coupled CTRW models, we can now\ncompute the limiting stochastic process (just like Brownian motion is the limit\nof a simple random walk), even in the case of heavy tailed (power-law) price\njumps and/or waiting times. The probability density functions for this limit\nprocess solve fractional partial differential equations. In some cases, these\nequations can be explicitly solved to yield descriptions of long-term price\nchanges, based on a high-resolution model of individual trades that includes\nthe statistical dependence between waiting times and the subsequent\nlog-returns. In the heavy tailed case, this involves operator stable space-time\nrandom vectors that generalize the familiar stable models. In this paper, we\nwill review the fundamental theory and present two applications with\ntick-by-tick stock and futures data.",
"arxiv_id": "physics/0608281",
"authors": [
"Mark M. Meerschaert",
"Enrico Scalas"
],
"categories": [
"physics.data-an",
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1016/j.physa.2006.04.034",
"journal_ref": "Physica A, vol. 370, 114-118, 2006",
"title": "Coupled continuous time random walks in finance",
"url": "https://arxiv.org/abs/physics/0608281"
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