Normal distribution

Statistics

Financial economics

Forward volatility

Physics

Skewness

Econometrics

Economics

Gaussian

Kurtosis

Generalized normal distribution

Cryptocurrency

Normal-inverse Gaussian distribution

Autoregressive conditional heteroskedasticity

Implied volatility

Volatility clustering

Mathematics

Computer security

Computer science

Gaussian random field

Gaussian process

Quantum mechanics

Financial models with long-tailed distributions and volatility clustering

Volatility (finance)

Quantitative Finance and Economics

Bitcoin has received a lot of attention from both investors and analysts, as it forms the highest market capitalization in the cryptocurrency market. This paper evaluates the volatility of Bitcoin returns using three GARCH models (sGARCH, iGARCH, and tGARCH). The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distribution in the return series of Bitcoin. Comparative to the Students't-distribution and the Generalized error distribution, the Normal Inverse Gaussian (NIG) distribution captured adequately the leptokurtic and skewness in all the GARCH models. The tGARCH model was the best model as it described the asymmetric occurrence of shocks in the Bitcoin market. That is, the response of investors to the same amount of good and bad news are distinct. From the empirical results, it can be concluded that tGARCH-NIG was the best model to estimate the volatility in the return series of Bitcoin. Generally, it would be optimal to use the NIG distribution in GARCH type models since time series of most cryptocurrency are leptokurtic.

Modelling the volatility of Bitcoin returns using GARCH models