Modern Rheology on a Stock Market: Fractional Dynamics of Indices

• Authors: M. Kozłowska , R. Kutner
• Languages of publication: EN

Abstracts

EN

This paper presents an exactly solvable (by applying the fractional calculus) the rheological model of fractional dynamics of financial market conformed to the principle of no arbitrage present on financial market. The rheological model of fractional dynamics of financial market describes some singular, empirical, speculative daily peaks of stock market indices, which define crashes as a kind of phase transition. In the frame of the model the plastic market hypothesis and financial uncertainty principle were formulated, which proposed possible scenarios of some market crashes. The brief presentation of the model was made in our earlier work (and references therein). The rheological model of fractional dynamics of financial market is a deterministic model and it is complementary to already existing other ones; together with them it offers possibility for thorough and widespread technical analysis of crashes. The constitutive, fractional integral equation of the model is an analogy of the corresponding one, which defines the fractional Zener model of plastic material. The fractional Zener model is the canonical one for modern rheology, polymer physics and biophysics concerning non-Debye relaxation of viscoelastic biopolymers. The useful approximate solution of the constitutive equation of the rheological model of fractional dynamics of financial market consists of two parts: (i) the first one connected with long-term memory present in the system, which is proportional to the generalized exponential function defined by the Mittag-Leffler function and (ii) the second one describing oscillations (e.g. beats or oscillations having two slightly shifted frequences). The shape exponent leading the Mittag-Leffler function, defines here the order of the phase transition between bullish and bearish states of the financial market, in particular, for recent hossa and bessa on some small, middle and large stock markets. It happened that this solution also successfully estimated some long-term price dynamics on the hypothetical market in United States.

Keywords

EN

89.20.-a; 89.65.-s; 89.65.Gh; 89.90.+n

Discipline

• 89.65.-s: Social and economic systems
• 89.20.-a: Interdisciplinary applications of physics
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 89.90.+n: Other topics in areas of applied and interdisciplinary physics (restricted to new topics in section 89)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 118
• Issue: 4
• Pages: 677-687

Dates

published

2010-10

received

2010-01-29

Contributors

author

M. Kozłowska

• Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University, Smyczkowa Str. 5/7, PL-02-678 Warsaw, Poland

author

R. Kutner

• Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University, Smyczkowa Str. 5/7, PL-02-678 Warsaw, Poland

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Identifiers

DOI

10.12693/APhysPolA.118.677