Econophysics Research in Victor Yakovenko's group

Collaborators

Papers

1. Statistical Mechanics of Money, Income, and Wealth

[1.1] "Statistical mechanics of money" by A. A. Dragulescu and V. M. Yakovenko

Published:  The European Physical Journal B, v. 17, pp. 723-729 (2000),  pdf
Preprint:  cond-mat/0001432, pdf.  Viewgraphs:  pdf
Computer Animation Video by Justin Chen
Computer Simulations in Mathematica by Ian Wright
Abstract:  In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Gibbs distribution emerges in computer simulations of economic models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Gibbs law does not hold.

[1.2] "Evidence for the exponential distribution of income in the USA" by A. A. Dragulescu and V. M. Yakovenko

Published:  The European Physical Journal B, v. 20, pp. 585-589 (2001),  pdf
Preprint:  cond-mat/0008305, pdf.  Viewgraphs:  pdf
Abstract:  Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2=50% agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=37.5% calculated for two-earners families.

[1.3] "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States" by A. A. Dragulescu and V. M. Yakovenko

Published:  Physica A, v. 299, pp. 213-221 (2001),  pdf
Preprint:  cond-mat/0103544, pdf.  Viewgraphs:  pdf
Abstract:  We present the data on wealth and income distributions in the United Kingdom, as well as on the income distributions in the individual states of the USA. In all of these data, we find that the great majority of population is described by an exponential distribution, whereas the high-end tail follows a power law. The distributions are characterized by a dimensional scale analogous to temperature. The values of temperature are determined for the UK and the USA, as well as for the individual states of the USA.

[1.4] "Statistical Mechanics of Money, Income, and Wealth: A Short Survey" by A. A. Dragulescu and V. M. Yakovenko

Published:  Modeling of Complex Systems: Seventh Granada Lectures, AIP Conference Proceedings 661, New York, 2003, pp. 180-183,  pdf
Preprint:  cond-mat/0211175, pdf.  Viewgraphs:  pdf
Abstract:  In this short paper, we overview and extend the results of our papers cond-mat/0001432, cond-mat/0008305, and cond-mat/0103544, where we use an analogy with statistical physics to describe probability distributions of money, income, and wealth in society. By making a detailed quantitative comparison with the available statistical data, we show that these distributions are described by simple exponential and power-law functions.

[1.5] "Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001" by A. C. Silva and V. M. Yakovenko

Published:  Europhysics Letters, v. 69, pp. 304-310 (2005),  pdf
Preprint:  cond-mat/0406385, pdf.  Presentation:  Viewgraphs, Video, and Audio online.
Abstract:  Personal income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs ("thermal") distribution, whereas the upper class (1-3% of population) has a Pareto power-law ("superthermal") distribution. By analyzing income data for 1983-2001, we show that the "thermal" part is stationary in time, save for a gradual increase of the effective temperature, whereas the "superthermal" tail swells and shrinks following the stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of population.

[1.6] "Two-class structure of income distribution in the USA: Exponential bulk and power-law tail" by V. M. Yakovenko and A. C. Silva

Published:  In the book "Econophysics of Wealth Distributions", edited by A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti (2005, Springer series "New Economic Windows", ISBN 88-470-0329-6), pp. 15-23
Abstract:  Conference proceedings paper based on [1.5].

[1.7] "A study of the personal income distribution in Australia" by A. Banerjee, V. M. Yakovenko, and T. Di Matteo

Published:  Physica A, v. 370, pp. 54-59 (2006),  pdf
Preprint:  physics/0601176, pdf. 
Abstract:  We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution.

2. Stochastic Volatility Models for Stock-Price Fluctuations

[2.1] "Probability distribution of returns in the Heston model with stochastic volatility" by A. A. Dragulescu and V. M. Yakovenko

Published:  Quantitative Finance, v. 2, pp. 443-453 (2002),  pdf.  Erratum:  Quantitative Finance, v. 3, p. C15 (2003),  pdf
Preprint:  cond-mat/0203046, pdf.  Viewgraphs:  vertical.pdf, horizontal.pdf,
Abstract:  We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow-Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data for 1982–2001 follow the scaling function for seven orders of magnitude.

[2.2] "Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes" by A. C. Silva and V. M. Yakovenko

Published:  Physica A 324, 303-310 (2003),  pdf
Preprint:  cond-mat/0211050, pdf.  Viewgraphs:  pdf
Abstract:  We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dragulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982-1999, we find a very good agreement between the theory and the data for a wide range of time lags from 1 to 250 days. On the other hand, deviations start to appear when the data for 2000-2002 are included. We interpret this as a statistical evidence of the major change in the market from a positive growth rate in 1980s and 1990s to a negative rate in 2000s.

[2.3] "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact" by A. C. Silva, R. E. Prange, and V. M. Yakovenko

Published:  Physica A 344, 227-235 (2004),  pdf
Preprint:  cond-mat/0401225, pdf.  Presentation:  ppt.
Abstract:  We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.

[2.4] "Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study" by A. C. Silva, and V. M. Yakovenko

Published:  Physica A 382, 278–285 (2007),  pdf
Preprint:  physics/0608299, pdf.  Presentation:  ppt.
Abstract:  We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.

3. Reviews Papers and Books on Econophysics

[3.1] "Applications of physics to economics and finance: Money, income, wealth, and the stock market" by A. A. Dragulescu

Posted: (2003) cond-mat/0307341, pdf.
Abstract:  Ph.D. thesis in physics defended on May 15, 2002 at the University of Maryland.  It covers the papers [1.1-1.4, 2.1] listed above and contains extra material.  (30 pages, 30 figures)

[3.2] "Research in econophysics" by V. M. Yakovenko

Posted:  (2003) cond-mat/0302270, pdf.
Abstract:  Review of econophysics research in the group of Victor Yakovenko written for the online newspaper published by the Department of Physics, University of Maryland: The Photon, Issue 24, January-February 2003

[3.3] "Applications of physics to finance and economics: returns, trading activity and income" by A. Christian Silva

Posted:  (2005) physics/0507022, pdf.
Abstract:  Ph.D. thesis in physics defended on May 10, 2005 at the University of Maryland. It covers the papers [2.2-2.3, 1.5] listed above and contains much additional material.  (24 pages, 45 figures)

[3.4] "Econophysics, Statistical Mechanics Approach to" by V. M. Yakovenko

Posted:  (2007) arXiv:0709.3662, pdf.
Published:  in Encyclopedia of Complexity and System Science, edited by R. A. Meyers, ISBN 978-0-387-75888-6, Springer (2009)
Abstract:  This invited review article surveys statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.  (24 pages, 11 figures, 144 citations)

[3.5] "Classical Econophysics" by A. F. Cottrell, P. Cockshott, G. J. Michaelson, I. P. Wright, and V. M. Yakovenko

Published:  series Advances in Experimental and Computable Economics, ISBN 978-0-415-47848-9, Routledge (2009)
Abstract:  This monograph examines the domain of classical political economy using the methodologies developed in recent years both by the new discipline of econophysics and by computing science. This approach is used to re-examine the classical subdivisions of political economy: production, exchange, distribution and finance. Covering a combination of techniques drawn from three areas, classical political economy, theoretical computer science and econophysics, to produce models that deepen our understanding of economic reality, this new title will be of interest to higher level doctoral and research students, as well as scientists working in the field of econophysics.  (384 pages)

[3.6] "Colloquium: Statistical Mechanics of Money, Wealth, and Income" by V. M. Yakovenko and J. B. Rosser, Jr.

Posted:  (2009) arXiv:0905.1518, pdf.
Accepted:  Reviews of Modern Physics.  Presentation:  Viewgraphs, Video, Audio, and Animation online.
Abstract:  The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

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Last updated May 23, 2009
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