Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes

Abootaleb Shirvani, Stefan Mittnik, William Brent Lindquist, Svetlozar Rachev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Article number82
JournalRisks
Volume12
Issue number5
DOIs
StatePublished - May 2024

Keywords

  • bitcoin volatility
  • intrinsic time
  • subordinated Lévy processes

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