Microscopic origin of non-Gaussian distributions of financial returns

T. Bíró, R. Rosenfeld

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.

Original languageEnglish
Pages (from-to)1603-1612
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Volume387
Issue number7
DOIs
Publication statusPublished - Mar 1 2008

Fingerprint

Stochastic Volatility Model
volatility
Born Approximation
Stochastic Volatility
Scaling Relations
t-distribution
Equilibrium Distribution
Time Lag
Approximation
Probability Density
Model
Volatility
Probability Distribution
scaling
Scaling
Born-Oppenheimer approximation
Verify
approximation
Zero
students

Keywords

  • Born-Oppenheimer approximation
  • Power-law distribution of returns
  • Stochastic volatility

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Microscopic origin of non-Gaussian distributions of financial returns. / Bíró, T.; Rosenfeld, R.

In: Physica A: Statistical Mechanics and its Applications, Vol. 387, No. 7, 01.03.2008, p. 1603-1612.

Research output: Contribution to journalArticle

@article{c7197ca439594b59834d24e85f674233,
title = "Microscopic origin of non-Gaussian distributions of financial returns",
abstract = "In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.",
keywords = "Born-Oppenheimer approximation, Power-law distribution of returns, Stochastic volatility",
author = "T. B{\'i}r{\'o} and R. Rosenfeld",
year = "2008",
month = "3",
day = "1",
doi = "10.1016/j.physa.2007.10.067",
language = "English",
volume = "387",
pages = "1603--1612",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "7",

}

TY - JOUR

T1 - Microscopic origin of non-Gaussian distributions of financial returns

AU - Bíró, T.

AU - Rosenfeld, R.

PY - 2008/3/1

Y1 - 2008/3/1

N2 - In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.

AB - In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.

KW - Born-Oppenheimer approximation

KW - Power-law distribution of returns

KW - Stochastic volatility

UR - http://www.scopus.com/inward/record.url?scp=37349089091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37349089091&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2007.10.067

DO - 10.1016/j.physa.2007.10.067

M3 - Article

AN - SCOPUS:37349089091

VL - 387

SP - 1603

EP - 1612

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 7

ER -