Article

# Dynamics of the return distribution in the Korean financial market

arXiv.org, Quantitative Finance Papers 01/2005;

Source: RePEc

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**ABSTRACT:**Publisher’s description: Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling, permit an understanding of the global behavior of economic systems without first having to work out a detailed microscopic description of the system. This pioneering text explores the use of these concepts in the description of financial systems, the dynamic new specialty of econophysics. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully-developed turbulent fluids and apply them to financial time series. They also present a new stochastic model that displays several of the statistical properties observed in empirical data. Physicists will find the application of statistical physics concepts to economic systems fascinating. Economists and other financial professionals will benefit from the book’s empirical analysis methods and well-formulated theoretical tools that will allow them to describe systems composed of a huge number of interacting subsystems. See the review of the second edition (2007; Zbl 1134.91001).12/2000; Cambridge University Press. - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper reports several entirely new results on financial market dynamics and option pricing. We observe that empirical distributions of returns are much better approximated by an exponential distribution than by a Gaussian. This exponential distribution of asset prices can be used to develop a new pricing model for options (in closed algebraic form) that is shown to provide valuations that agree very well with those used by traders. We show how the Fokker–Planck formulation of fluctuations can be used with a local volatility (diffusion coefficient) to generate an exponential distribution for asset returns, and also how fat tails for extreme returns are generated dynamically by a simple generalization of our new volatility model. Nonuniqueness in deducing dynamics from empirical data is discussed and is shown to have no practical effect over time scales much less than one hundred years. We derive an option pricing pde and explain why it is superfluous, because all information required to price options in agreement with the delta-hedge is already included in the Green function of the Fokker–Planck equation for a special choice of parameters. Finally, we also show how to calculate put and call prices for a stretched exponential returns density.Physica A: Statistical Mechanics and its Applications 02/2003; · 1.72 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this opening talk, we discuss some of the similarities between work being done by economists, and by physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken, and justify these different approaches by developing the argument that by approaching the same problem from different points of view new results might emerge. In particular, we review some recent results, for example the finding that there are two new universal scaling models in economics: (i) the fluctuation of price changes of any stock market is characterized by a PDF which is a simple power law with exponent 4 that extends over 102 standard deviations (a factor of 108 on the y-axis); (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈1/6. Neither of these two new laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations.Physica A: Statistical Mechanics and its Applications 01/2001; · 1.72 Impact Factor

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