Short Comprehensive Report on the Non-Brownian Stochastic Dynamics at Financial and Commodity Markets

• Authors: T. Ciepliński , A. Dominiczak , R. Kutner
• Languages of publication: EN

Abstracts

EN

In this work we empirically verify the generic breaking of the Central Limit Theorem on the financial and commodity markets. We analysed the distributions of log-returns for typical indices and price of gold, for increasing time horizons. We considered Random Coarse Graining Transformation of the Continuous-Time Random Walk model, which can represent the non-Gaussian price dynamics of underlying assets and the corresponding derivatives, e.g., various options or future contracts. We confirmed that empirical data and predictions of the model quite well agree.

Keywords

EN

89.20.-a   89.65.Gh   02.50.Ey   02.50.Ga   05.40.Fb  

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 2B
• Pages: B-24-B-27

Dates

published

2012-02

References

• [1] R.N. Mantegna, Physica A 179, 232 (1991)
• [2] R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics. Correlations and Complexity in Finance, Cambridge Univ. Press, Cambridge 2000
• [3] J. Bernstein, Am. J. Phys. 73, 395 (2005)
• [4] R. Merton, J. Finance 29, 449 (1973)
• [5] R. Merton, Continuous-Time Finance, Basil Blackwell, Oxford 1990
• [6] F. Black, J. Portfolio Management 15, 4 (1995)
• [7] P.A. Samuelson, Industrial Management Rev. 6, 13 (1965)
• [8] J.C. Cox, S.A. Ross, M. Rubistein, J. Financial Economics 7, 229 (1979)
• [9] W. Schoutens, Lévy Processes in Finance. Pricing Financial Derivatives in Wiley Series in Probability and Statistics, Wiley, Chichester 2003
• [10] S.I. Boyarchenko, S.Z. Levendorskii, Non-Gaussian, Merton-Black-Scholes Theory in Advanced Series on Statistical Science & Applied Probability, World Sci., New Jersey 2002
• [11] A. Kyprianou, W. Schoutens, P. Wilmott, Exotic Option Pricing and Advanced Lévy Models, Wiley, Chichester 2005
• [12] Extreme Events in Nature and Society, Eds. S. Albeverio, V. Jentsch, H. Kantz in Frontiers Collection, Springer-Verlag, Berlin 2006
• [13] A. Kasprzak, R. Kutner, J. Perelló, J. Masoliver, EPJ B 76, 513 (2010)
• [13] A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69, 026105 (2004)
• [14] S. Wolfram, A New Kind of Science, Wolfram Media Inc., Champaign 2002
• [15] A. Jurlewicz, A. Wołymańska, P. Żebrowski, Acta Phys. Pol. A, 114, 629 (2008)
• [16] A. Jurlewicz, A. Wołymańska, P. Żebrowski, Physica A, 388, 407 (2009)
• [17] www.stockrageus.com: data for 10-minutes time interval; www.stooq.pl: other data

Identifiers

DOI

10.12693/APhysPolA.121.B-24