Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes

Abootaleb Shirvani (), Stefan Mittnik, William Brent Lindquist and Svetlozar Rachev
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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

Risks, 2024, vol. 12, issue 5, 1-21

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.

Keywords: bitcoin volatility; subordinated Lévy processes; intrinsic time (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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