TY - JOUR
T1 - Bitcoin Volatility and Intrinsic Time Using Double-Subordinated Lévy Processes
AU - Shirvani, Abootaleb
AU - Mittnik, Stefan
AU - Lindquist, William Brent
AU - Rachev, Svetlozar
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/5
Y1 - 2024/5
N2 - 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.
AB - 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.
KW - bitcoin volatility
KW - intrinsic time
KW - subordinated Lévy processes
UR - http://www.scopus.com/inward/record.url?scp=85193978935&partnerID=8YFLogxK
U2 - 10.3390/risks12050082
DO - 10.3390/risks12050082
M3 - Article
AN - SCOPUS:85193978935
SN - 2227-9091
VL - 12
JO - Risks
JF - Risks
IS - 5
M1 - 82
ER -