dorsal/arxiv
View SchemaAdditive-multiplicative stochastic models of financial mean-reverting processes
| Authors | C. Anteneodo, R. Riera |
|---|---|
| Categories | |
| ArXiv ID | physics/0502119 |
| URL | https://arxiv.org/abs/physics/0502119 |
| DOI | 10.1103/PhysRevE.72.026106 |
Abstract
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through a It\^o-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.
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"abstract": "We investigate a generalized stochastic model with the property known as mean\nreversion, that is, the tendency to relax towards a historical reference level.\nBesides this property, the dynamics is driven by multiplicative and additive\nWiener processes. While the former is modulated by the internal behavior of the\nsystem, the latter is purely exogenous. We focus on the stochastic dynamics of\nvolatilities, but our model may also be suitable for other financial random\nvariables exhibiting the mean reversion property. The generalized model\ncontains, as particular cases, many early approaches in the literature of\nvolatilities or, more generally, of mean-reverting financial processes. We\nanalyze the long-time probability density function associated to the model\ndefined through a It\\^o-Langevin equation. We obtain a rich spectrum of shapes\nfor the probability function according to the model parameters. We show that\nadditive-multiplicative processes provide realistic models to describe\nempirical distributions, for the whole range of data.",
"arxiv_id": "physics/0502119",
"authors": [
"C. Anteneodo",
"R. Riera"
],
"categories": [
"physics.soc-ph",
"cond-mat.stat-mech",
"q-fin.ST"
],
"doi": "10.1103/PhysRevE.72.026106",
"title": "Additive-multiplicative stochastic models of financial mean-reverting processes",
"url": "https://arxiv.org/abs/physics/0502119"
},
"schema_id": "dorsal/arxiv",
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