Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy\n Processes

2021/09/25 by Abootaleb Shirvani, Stefan Mittnik, Shirvani, Abootaleb +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · #Blockchain Technology Applications and Security #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2109.15051

openalex publication_date 2021/09/25 · openalex created_date 2023/09/01 · openalex updated_date 2026/07/28

Abstract

We propose a doubly subordinated Levy process, NDIG, to model the time series\nproperties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed\nproperties of bitcoin prices and gives rise to an arbitrage free, option\npricing model. In this framework we derive two bitcoin volatility measures. The\nfirst combines NDIG option pricing with the Cboe VIX model to compute an\nimplied volatility; the second uses the volatility of the unit time increment\nof the NDIG model. Both are compared to a volatility based upon historical\nstandard deviation. With appropriate linear scaling, the NDIG process perfectly\ncaptures observed, in-sample, volatility.\n

Citations

• Testing the null hypothesis of stationarity against the alternative of a unit root
• The Pricing of Options and Corporate Liabilities

Cited by

• Fast Likelihood-Free Parameter Estimation for Lévy Processes

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