The Leverage Effect and Other Stylized Facts Displayed by Bitcoin Returns

Abstract

In this paper, we explore some stylized facts of the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2020. Despite Bitcoin presenting some very peculiar idiosyncrasies, like the absence of macroeconomic fundamentals or connections with underlying assets or benchmarks, an asymmetry between demand and supply and the presence of inefficiency in the form of strong arbitrage opportunity, all these elements seem to be marginal in the definition of the structural statistical properties of this virtual financial asset, which result to be analogous to general individual stocks or indices. In contrast, we find some clear differences, compared to fiat money exchange rates time series, in the values of the linear autocorrelation and, more surprisingly, in the presence of the leverage effect. We also explore the dynamics of correlations, monitoring the shifts in the evolution of the Bitcoin market. This analysis is able to distinguish between two different regimes: a stochastic process with weaker memory signatures and closer to Gaussianity between the Mt. Gox incident and the late 2015, and a dynamics with relevant correlations and strong deviations from Gaussianity before and after this interval.

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Acknowledgments

F.N.M.S.F. received partial financial support from the PIBIC program of Universidade Federal do Rio de Janeiro. M.A.B. received support from Fapesp (Grant 2018/22562-4) and CNPQ (Grant 303986/2017-4 and 428433/2018-9).

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de Sousa Filho, F.N.M., Silva, J.N., Bertella, M.A. et al. The Leverage Effect and Other Stylized Facts Displayed by Bitcoin Returns. Braz J Phys (2021). https://doi.org/10.1007/s13538-020-00846-8

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Keywords

  • Fluctuation phenomena
  • Random processes
  • Noise
  • Brownian motion