Volatility estimation for Bitcoin: A comparison of GARCH models (original) (raw)

Modeling Volatility for High-Frequency Data of Cryptocurrency Bitcoin Price using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Model

The cryptocurrency namely Bitcoin is a decentralized cryptocurrency considered a type of digital asset that uses public-key cryptography to record, sign and send transactions over the Bitcoin blockchain. All transaction processes are performed without the oversight of a central authority. The time series data for Bitcoin price movement exhibit time-varying volatility and volatility clustering. This study aims to evaluate the time-varying volatility of Bitcoin price using the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. This study uses daily share prices starting from July 2017 until July 2022. The mean equation was developed using the ARMA (1,1) for Bitcoin return. Next, this study evaluated OLS, GARCH, GARCH-M, and E-GARCH models. The result shows the EGARCH (1,1) model exhibits its lowest error of AIC with a value of 5.5984. The autocorrelation test was performed using Q-statistics indicating EGARCH (1,1) model is free from the autocorrelation problem. In addition, ARCH-LM test indicates EGARCH (1,1) is free from heteroscedasticity problems. The EGARCH (1,1) shows there is a leverage effect for volatility clustering. This explained the behavior of bad news effect more than positive news. The finding of the study can act as a guideline to help investors to analyze their investment behavior. At the same time, the finding of this study helps investors to understand the cryptocurrency dynamics behavior.

Modelling the Volatility of the Price of Bitcoin

American Journal of Mathematics and Statistics, 2019

This study assessed the volatility and the Value at Risk (VaR) of daily returns of Bitcoins by conducting a comparative study in the forecast performance of symmetric and asymmetric GARCH models based on three different error distributions. The models employed are the SGARCH and TGARCH which were validated based on AIC, MAE and MSE measures. The results indicated that the SGARCHGED (1,1) with generalised error distribution term was identified as the best fitted GARCH model. Though, this best fitted model based on information loss (AIC) did not provide the best out-of-sample forecast, the differences was insignificant. Thus, the study clearly demonstrates that it is reliable to use the best fitted model for volatility forecasting. Also, to further validate the performance of the best fitted model, it was subjected to a historical back-test using Value at Risk (VaR). Though, it was evident from the study that no model was superior, it was indicated that an average loss of 1.2% is expe...

Analysis of Bitcoin Returns Volatility using AR-GARCH Modelling

SSRN Electronic Journal, 2020

Bitcoin is a virtual/cryptocurrency, serving as a decentralized medium of digital exchange and not tied to any financial institution. It gained in popularity in the aftermath of the global financial crisis with the failure of many prominent banks and financial institutions, as it provided investors with direct control over their money. The supply of Bitcoins is constrained due to its geometrically decreasing growth rate, with a limiting maximum supply of twenty-one million Bitcoins. Because of the limited number of Bitcoins in circulation and their increasing demand, Bitcoin prices tend to be highly volatile and increase/decrease at a very fast pace. Many noted economists have characterised Bitcoin prices as a speculative bubble. However, it is expected that, with wider acceptance and adoption of Bitcoins, Bitcoin prices would settle down and its volatility would stabilise. The study examines the stability of Bitcoin price/returns volatility using an AR-GARCH model. The data for the study were the daily closing Bitcoin prices obtained from the bitcoin,com website 1 for the study period 01/01/2013-31/12/2017.

Estimation of Bitcoin Volatility: GARCH Implementation

International Journal of Economics and Management Studies, 2020

As bitcoin is a topic of high interest for academic and professsional life over recent years, a number of literature has examined its the price movements, volatility and predictions. Bitcoin is the first and perhaps the most popular cryptocurrency with a high volatility pattern compared to the other cryptocurrencies. This paper examines the models that explains the volatility of Bitcoin prices. The daily data for the Bitcoin prices are used through a period of July 31, 2017 to April 3, 2019, a total number of observations of 484. Initially, unit root tests are implemented. Then, the heteroskedasticity problem is tested among variables. Based on results of the heteroskedasticity test, it is decided to use ARCH models. Then, ARCH, GARCH, TGARCH and EGARCH results are tested to find out the best fit model that explains the bitcoin price movements.

Modeling cryptocurrencies volatility using GARCH models: a comparison based on Normal and Student's T-Error distribution

Entrepreneurship and Sustainability Issues

This study measures the volatility of cryptocurrency by utilizing the symmetric (GARCH 1,1) and asymmetric (EGARCH, TGARCH, PGARCH) model of GARCH family using a daily database designated in different digital monetary standards. The results for an explicit set of currencies for entire period provide evidence of volatile nature of cryptocurrency and in most of the cases, the PGARCH is a better-fitted model with student's t distribution. The findings show positive shocks heavily affected conditional volatility as a contrast with negative stuns. Those additional analyses can be provided further support their findings and worthwhile information for economic thespians who are engrossed in adding cryptocurrency to their equity portfolios or are snooping about the capabilities of cryptocurrency as a financial asset.

Forecasting the Volatility of the Cryptocurrency Market by GARCH and Stochastic Volatility

Mathematics

This study examines the volatility of nine leading cryptocurrencies by market capitalization—Bitcoin, XRP, Ethereum, Bitcoin Cash, Stellar, Litecoin, TRON, Cardano, and IOTA-by using a Bayesian Stochastic Volatility (SV) model and several GARCH models. We find that when we deal with extremely volatile financial data, such as cryptocurrencies, the SV model performs better than the GARCH family models. Moreover, the forecasting errors of the SV model, compared with the GARCH models, tend to be more accurate as forecast time horizons are longer. This deepens our insight into volatility forecast models in the complex market of cryptocurrencies.

Modelling Volatility Dynamics of Cryptocurrencies Using GARCH Models

Journal of Mathematical Finance

Cryptocurrencies have become increasingly popular in recent years attracting the attention of the media, academia, investors, speculators, regulators, and governments worldwide. This paper focuses on modelling the volatility dynamics of eight most popular cryptocurrencies in terms of their market capitalization for the period starting from 7th August 2015 to 1st August 2018. In particular, we consider the following cryptocurrencies; Bitcoin, Ethereum, Litecoin, Ripple, Moreno, Dash, Stellar and NEM. The GARCH-type models assuming different distributions for the innovations term are fitted to cryptocurrencies data and their adequacy is evaluated using diagnostic tests. The selected optimal GARCH-type models are then used to simulate out-of-sample volatility forecasts which are in turn utilized to estimate the one-day-ahead VaR forecasts. The empirical results demonstrate that the optimal in-sample GARCH-type specifications vary from the selected out-of-sample VaR forecasts models for all cryptocurrencies. Whilst the empirical results do not guarantee a straightforward preference among GARCH-type models, the asymmetric GARCH models with long memory property and heavy-tailed innovations distributions overall perform better for all cryptocurrencies.

From Discrete to Continuous: Garch Volatility Modeling of the Bitcoin

Ege Akademik Bakis (Ege Academic Review)

Volatility is an important concept for identifying and predicting the risk of financial products. The aim of the study is to determine the most appropriate discrete model for the volatility of Bitcoin returns using the discrete-time GARCH model and its extensions and compare it with the Lévy driven continuous-time GARCH model. For this purpose, the volatility of Bitcoin returns is modeled using daily data of Bitcoin / United States Dolar exchange rate. By comparing discrete-time models according to information criteria and likelihood values, the All-GARCH model with Johnson's-SU innovations is found to be the most adequate model. The persistence of the volatility and half-life of the volatility of the returns are calculated according to the estimation of the discrete model. This discrete model has been compared with the continuous model in which the Lévy increments are derived from the compound Poisson process using various error measurements. As a conclusion, it is found that t...

The predictive capacity of GARCH-type models in measuring the volatility of crypto and world currencies

PLOS ONE, 2021

This paper provides a thorough overview and further clarification surrounding the volatility behavior of the major six cryptocurrencies (Bitcoin, Ripple, Litecoin, Monero, Dash and Dogecoin) with respect to world currencies (Euro, British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen), the relative performance of diverse GARCH-type specifications namely the SGARCH, IGARCH (1,1), EGARCH (1,1), GJR-GARCH (1,1), APARCH (1,1), TGARCH (1,1) and CGARCH (1,1), and the forecasting performance of the Value at Risk measure. The sampled period extends from October 13th 2015 till November 18th 2019. The findings evidenced the superiority of the IGARCH model, in both the in-sample and the out-of-sample contexts, when it deals with forecasting the volatility of world currencies, namely the British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen. The CGARCH alternative modeled the Euro almost perfectly during both periods. Advanced GARCH mo...