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Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach

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  • Mariusz Tarnopolski

Abstract

The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst exponent $H>0.5$, is exploited in order to predict future BTC/USD price. A Monte Carlo simulation with $10^4$ geometric fractional Brownian motion realisations is performed as extensions of historical data. The accuracy of statistical inferences is 10\%. The most probable Bitcoin price at the beginning of 2018 is 6358 USD.

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  • Mariusz Tarnopolski, 2017. "Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach," Papers 1707.03746, arXiv.org, revised Aug 2017.
    • Handle: RePEc:arx:papers:1707.03746
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    1. Paolo Angelis & Roberto Marchis & Mario Marino & Antonio Luciano Martire & Immacolata Oliva, 2021. "Betting on bitcoin: a profitable trading between directional and shielding strategies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 883-903, December.
    2. Vladimir Soloviev & Andrey Belinskiy, 2018. "Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors," Papers 1807.05837, arXiv.org, revised Jul 2018.
    3. Jules Clément Mba & Sutene Mwambetania Mwambi & Edson Pindza, 2022. "A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process," Forecasting, MDPI, vol. 4(2), pages 1-11, March.
    4. Vasile Brătian & Ana-Maria Acu & Camelia Oprean-Stan & Emil Dinga & Gabriela-Mariana Ionescu, 2021. "Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion," Mathematics, MDPI, vol. 9(22), pages 1-20, November.

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