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Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes

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  • Abootaleb Shirvani
  • Stefan Mittnik
  • W. Brent Lindquist
  • Svetlozar T. Rachev

Abstract

We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices 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 Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.

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  • Abootaleb Shirvani & Stefan Mittnik & W. Brent Lindquist & Svetlozar T. Rachev, 2021. "Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes," Papers 2109.15051, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2109.15051
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    Cited by:

    1. Yifan He & Abootaleb Shirvani & Barret Shao & Svetlozar Rachev & Frank Fabozzi, 2024. "Beyond the Bid-Ask: Strategic Insights into Spread Prediction and the Global Mid-Price Phenomenon," Papers 2404.11722, arXiv.org, revised Oct 2024.

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