Abstract
Analysis of time-series data of different markets have produced evidence for several stylized facts (universal features) including heavy tails characterized by power law exponents, which provide us tantalizing hints of the dynamics underlying such complex systems. It is especially important to see how these features evolve over time after the market is created and gradually develops. The recent advent of the digital currency, Bitcoin, and its growing popularity as an asset traded between agents over the last few years, provides us with an invaluable dataset for such a study. Similar to many financial markets, Bitcoin is de-centralized and its value is not controlled by a single institution, (e.g., a central bank). Here we have analyzed high-frequency Bitcoin trading data (with a resolution of one tick, i.e., a single trading event). We show that the distribution of price fluctuation (measured in terms of logarithmic return) has a heavy tail. The exponent of the tail implies that Bitcoin fluctuations follow an inverse square law, in contrast to the inverse cubic law exhibited by most financial and commodities markets. The distribution of transaction sizes and trading volume are seen to have Levy-stable distribution. Multi-scale analysis show the presence of long term memory effects in market behavior.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
S. Sinha, A. Chatterjee, A. Chakraborti, B.K. Chakrabarti, Econophysics: An Introduction (Wiley, Weinheim, 2011)
R.N. Mantegna, Z. Palágyi, H.E. Stanley, Applications of statistical mechanics to finance. Phys. A 274, 216–221 (1999)
T. Lux, The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks. Appl. Financ. Econ. 6, 463–475 (1996)
D.W. Jansen, C.G. De Vries, On the frequency of large stock returns: putting booms and busts into perspective. Rev. Econ. Stat. 73, 18–24 (1991)
P. Gopikrishnan, M. Meyer, L.A.N. Amaral, H.E. Stanley, Inverse cubic law for the distribution of stock price variations. Eur. Phys. J. B 3, 139–140 (1998)
R.K. Pan, S. Sinha, Self-organization of price fluctuation distribution in evolving markets. EPL 77, 58004 (2007)
S.V. Vikram, S. Sinha, Emergence of universal scaling in financial markets from mean-field dynamics. Phys. Rev. E 83, 016101 (2011)
Acknowledgments
We thank Frederic Abergel and Arnab Chatterjee for helpful discussions. This work is supported in part by the Department of Atomic Energy through the IMSc Econophysics (XII Plan ) Project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Easwaran, S., Dixit, M., Sinha, S. (2015). Bitcoin Dynamics: The Inverse Square Law of Price Fluctuations and Other Stylized Facts. In: Abergel, F., Aoyama, H., Chakrabarti, B., Chakraborti, A., Ghosh, A. (eds) Econophysics and Data Driven Modelling of Market Dynamics. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-319-08473-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-08473-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08472-5
Online ISBN: 978-3-319-08473-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)