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Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach

Author

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  • Grilli, Luca
  • Santoro, Domenico

Abstract

In this paper we try to build a statistical ensemble to describe a cryptocurrency-based system, emphasizing an "affinity" between the system of agents trading in these currencies and statistical mechanics. We focus our study on the concept of entropy in the sense of Boltzmann and we try to extend such a definition to a model in which the particles are replaced by N agents completely described by their ability to buy and to sell a certain quantity of cryptocurrencies. After providing some numerical examples, we show that entropy can be used as an indicator to forecast the price trend of cryptocurrencies.

Suggested Citation

  • Grilli, Luca & Santoro, Domenico, 2020. "Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach," MPRA Paper 99591, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:99591
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    References listed on IDEAS

    as
    1. Campbell, John & Shiller, Robert, 1988. "Stock Prices, Earnings, and Expected Dividends," Scholarly Articles 3224293, Harvard University Department of Economics.
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    3. Les Gulko, 1999. "The Entropy Theory Of Stock Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 331-355.
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    5. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    6. McCauley, Joseph l., 2004. "Thermodynamic analogies in economics and finance: instability of markets," MPRA Paper 2159, University Library of Munich, Germany.
    7. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-980, July.
    8. repec:bla:jfinan:v:43:y:1988:i:3:p:661-76 is not listed on IDEAS
    9. Mihály Ormos & Dávid Zibriczky, 2014. "Entropy-Based Financial Asset Pricing," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-21, December.
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    Cited by:

    1. Grilli, Luca & Santoro, Domenico, 2020. "Dualism in Bitcoin Dynamics: existence of an Upper Bound in Poincaré Recurrence Theorem for Deterministic vs Stochastic Behavior," MPRA Paper 101057, University Library of Munich, Germany.
    2. Grilli, Luca & Santoro, Domenico, 2020. "How Boltzmann Entropy Improves Prediction with LSTM," MPRA Paper 100578, University Library of Munich, Germany.

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    Keywords

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G19 - Financial Economics - - General Financial Markets - - - Other

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