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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 7: Financial Markets and Risk Management II

AKSOE 7.3: Vortrag

Dienstag, 28. März 2006, 15:00–15:30, BAR 205

Dynamics of Warsaw Stock Exchange index as analysed by the Mittag-Leffler function — •Marzena Kozlowska and Ryszard Kutner — Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University

We studied the historical Warsaw Stock Exchange (WSE) index (WIG) at a daily time horizon; we expect that its dynamics is typical for an emerging financial market of moderate size. We found that the well developed maxima of the index can be fitted (up to its fluctuations) by an intermediate part of the Mittag-Leffler (ML) function which is a natural generalisation of the exponential one.

Note that the ML function has two characteristic limits: (i) the stretched exponential form or Kohlrausch-Williams-Watts (KWW) law for the initial times, and (ii) the power-law or the Nuttig law for the asymptotic time. These decays are typical for the relaxation of disorder systems.

In other words, the relaxation of the WIG local maxima can be described by the fractional (non-Debye) relaxation equation which has indeed the solution given by the ML function.

Since we found that most of the empirical WIG maxima are well covered by the intermediate part of the ML function, this means that the WSE is a complex system lying between two different types of disordered ones created by stock market investors and described, correspondingly, by two types of relaxation functions (i) and (ii). Unfortunately, this observation does not uniquely define the microeconomical (or microscopic) model which constitutes its basis.