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Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes

Author

Listed:
  • Abootaleb Shirvani

    (Department of Mathematical Science, Kean University, Union, NJ 07083, USA)

  • Stefan Mittnik

    (Department of Statistics, Ludwig Maximilians University, 80539 Munchen, Germany)

  • William Brent Lindquist

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409, USA)

  • Svetlozar Rachev

    (Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409, USA)

Abstract

We propose a doubly subordinated Lévy process, the normal double inverse Gaussian (NDIG), to model the time series properties of the cryptocurrency bitcoin. By using two subordinated processes, NDIG captures both the skew and fat-tailed properties of, as well as the intrinsic time driving, bitcoin returns and gives rise to an arbitrage-free option pricing model. In this framework, we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Chicago Board Options Exchange VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both volatility measures are compared to the volatility based on the historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures the observed in-sample volatility.

Suggested Citation

  • Abootaleb Shirvani & Stefan Mittnik & William Brent Lindquist & Svetlozar Rachev, 2024. "Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes," Risks, MDPI, vol. 12(5), pages 1-21, May.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:5:p:82-:d:1398008
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