Entropy Approach for Volatility of Ethereum and Bitcoin
Keywords:Shannon Entropy, Tsallis entropy, RÃ©nyi entropy, Approximate entropy, Crypto Money
The application of entropy in finance can be regarded as the extension of information entropy and probability theory. In this article we apply the concept of entropy for basic crypto money (Ethereum and Bitcoin) to make a comparison. We compute in the first step Shannon entropy with different estimators, Tsallis entropy for different values of its parameter, RÃ©nyi entropy and at last the approximate entropy. We provide computational results for these entropies for daily data.
Laidler, K.J., Thermodynamics, In The World of Physical Chemistry, Oxford University Press, New York, NY, USA, pp. 156â€“240,1995.
Tsallis, C., â€œPossible generalization of Boltzmann-Gibbs statisticsâ€, Journal of Statistical Physics, 52,479-487,1988.
Rao, M.,Chen, Y.,Vemuri, B.C., & Wang, F., Cumulative residual entropy: a new measure of information , IEEE transactions on Information Theory, 50(6), 1220-1228, 2004.
Shafee, F., â€œLambert function and a new non-extensive form of entropyâ€, IMA journal of applied mathematics, 72(6), 785-800, 2007.
Pincus, S., Approximate entropy as an irregularity measure for financial data, Econometric Reviews, 27(4-6), 329-362, 2008.
Ubriaco, M. R., Entropies based on fractional calculus, Physics Letters A, 373(30), 2516-2519, 2009.
Rompolis, L. S., â€œRetrieving risk neutral densities from European option prices based on the principle of maximum entropyâ€, Journal of Empirical Finance, 17(5), 918-937, 2010.
Wang, G. J., Xie, C., & Han, F., Multi-scale approximate entropy analysis of foreign exchange markets efficiency, Systems Engineering Procedia, 3, 201-208, 2012.
Ormos, M., & Zibriczky, D., Entropy-based financial asset pricing, PloS one, 9(12), e115742, 2014.
Van Erven, T., & Harremos, P., RÃ©nyi divergence and Kullback-Leibler divergence, IEEE Transactions on Information Theory, 60(7), 3797-3820, 2014.
Niu, H., & Wang, J., Quantifying complexity of financial short-term time series by composite multiscale entropy measure. Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 375-382, 2015.
Dedu, S., & Toma, A., An Integrated Risk Measure And Information Theory Approach For Modeling Financial Data And Solving Decision Making Problems, Procedia Economics and Finance, 22, 531-537, 2015.
Sati, M. M., & Gupta, N., â€œSome characterization results on dynamic cumulative residual Tsallis entropyâ€, Journal of Probability and Statistics, 2015.
Stosic, D., Stosic, D., Ludermir, T., de Oliveira, W., & Stosic, T., Foreign exchange rate entropy evolution during financial crises. Physica A: Statistical Mechanics and its Applications, 449, 233-239,2016.
Ponta, L., & Carbone, A., Information measure for financial time series: quantifying short-term market heterogeneity, Physica A: Statistical Mechanics and its Applications, 2018.
Khammar, A. H., & Jahanshahi, S. M. A., On weighted cumulative residual Tsallis entropy and its dynamic version, Physica A: Statistical Mechanics and its Applications, 491, 678-692, 2018.
Nakamoto, S., Bitcoin: A peer-to-peer electronic cash system, 2008.
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