مالیات پیاده نرمال شده کوتاه به کار گرفته در مطالعه شاخص های مالی

This work is devoted to the study of the statistical properties of financial indices from developed and emergent markets. We performed a new analysis of the behavior of several financial indices by using a normalized truncated Levy walk model. We conclude that the truncated Levy distribution describes perfectly the evolution of the financial indices near a crash for both well-developed and emergent markets.

In recent years a new discipline: econophysics, has been developed [1]. This discipline was introduced in 1995, see Ref. [2]. It studies the application of mathematical tools that are usually applied to physical models, to the study of financial models. Simultaneously, there has been a growing literature in financial economics analyzing the behavior of major stock indices [3], [4], [5], [6] and [7]. The Statistical Mechanics theory and models, like phase transitions and critical phenomena models, have been applied by many authors to the study of the speculative bubbles preceding a financial crash (see for example Refs. [8] and [9]). In these works the main assumption is the existence of log-periodic oscillation in the data. The scale invariance in the behavior of financial indices near a crash has been studied in Refs. [10] and [11]. The statistical properties of the temporal series analyzing the evolution of the different markets have been of great importance in the study of financial indices. The empirical characterization of stochastic processes usually requires the study of temporal correlations and the determination of asymptotic probability density functions (pdf). The first model describing the option prices evolution is the Brownian motion. This model assumes that the increment in the logarithm of the prices follows a diffusive process with Gaussian distribution [12]. However, the empirical study of the temporal series associated to some of the most important financial indices shows that in short time intervals the associated pdf has greater kurtosis than a Gaussian distribution [6], and that the Brownian motion does not describe accurately the evolution of financial indices near a crash. The first step in order to explain this behavior was done in 1963 by Mandelbrot [13]. He developed a stochastic model for the evolution of the cotton price by using a stable non-Gaussian Levy process [14]. However, these distributions are not appropriated for working in long-range correlation scales. These problems can be avoided considering that the temporal evolution of financial markets is described by a Truncated Levy Flight (TLF) [15] and [16]. Most of the studies mentioned before have been done with financial indices of developed markets that have a great volume of transactions. In this work we analyze financial indices corresponding to developed and emergent markets. Our main interest is to verify that the TLF distribution describes accurately the behavior of financial indices for both developed and emergent markets. The presentation is organized as follows. In section 2, we give a short introduction to the Levy distributions. In section 3, we present the indices that will be analyzed and the normalized Levy model that will be used for our numerical analysis. Finally, in section 3, we conclude that our results are perfectly compatible with a TLF distribution.