Advanced GARCH Specifications for Cryptocurrency Volatility Incorporating Asymmetry, Regime-Switching, and Long-Memory Effects

In this study, the impact of volatility regime shifts on volatility persistence and hedge ratio estimation is determined for four major currencies using an iterated cumulative sums of squares (ICSS)-GARCH model. Employing a standard GARCH (1,1) model as the benchmark, within-sample results demonstrate that the inclusion of volatility shifts substantially reduces volatility persistence and the significance of the ARCH and GARCH coefficients. In terms of hedging effectiveness, the ICSS-GARCH model outperforms the standard GARCH model for all four currencies. In comparison to two constant volatility models, the standard GARCH model yields the lowest performance, whereas the ICSS-GARCH model performs at least as well as these models. In out-of-sample analysis, the GARCH model provides substantial variance reductions relative to the constant volatility models. Moreover, the ICSS-GARCH model yields positive variance reductions relative to all competing models, including the standard GARCH model. The results suggest that in cases where dynamic hedging is important, sudden shifts in volatility should not be ignored.

This research examines the performance of return and volatility models on the long-memory, asymmetric volatility, and leverage effects by comparing the two most active futures markets globally, Currency and Index Futures. The study uses daily data from the database Quandl.com website, from January 2000 to March 2018. This study utilizes two short-memory models, the autoregressive moving average – exponential generalized autoregressive conditional heteroskedasticity (ARMA-EGARCH); and autoregressive moving average – asymmetric power autoregressive conditional heteroskedasticity (ARMA-APARCH); and two long-memory models, autoregressive fractionally-integrated moving average – fractionally-integrated exponential generalized autoregressive conditional heteroskedasticity (ARFIMA-FIEGARCH); and autoregressive fractionally-integrated moving average – fractionally-integrated asymmetric power autoregressive conditional heteroskedasticity (ARFIMA-FIAPARCH). The paper shows that portfolio managers and traders can benefit in holding Index futures, because of their steady returns, but with a relatively higher risk for the whole sample period. The study also finds that Currency futures has better safe-haven properties during crisis period, but Index futures performs better after crisis period. Findings suggest that both long-memory models are capable of accurate forecast, especially on the volatility of Currency and Index futures. The proper modelling of Currency and Index futures time-series data can provide traders, fund managers and investors in creating well-defined trading strategies, especially in high volatility regimes.

<abstract> <p>The aim of this study was to examine the returns and volatility of Bitcoin. The study uses the daily closing price of Bitcoin from October 1, 2013 to July 31, 2020 as the sample data, which include 2496 observations. About the methodology, the paper describes the utilisation of GARCH models to analyse Bitcoin's returns and volatility. First, the data were tested by using the augmented Dickey-Fuller test to verify the stability and diagram tests sequence. After that, the lag order and determination results of the mean value equation show that the Lag 4 period is the best. Additionally, the paper describes an autocorrelation test of the residual series, which revealed that there is no significant autocorrelation in the residual term for the Bitcoin returns, but that the residual squared has significant autocorrelation. In addition, a linear graph of squared residuals was formulated and the ARCH-LM test was used to find the data that are suitable for modelling with GARCH models since the data have a strong ARCH effect. As result, a GARCH (1, 1) model was used; the findings indicated that the returns and volatility of Bitcoin have clustering characteristics, and that the returns and volatility of Bitcoin constitute a persistent process although the effects gradually reduce over time. Because of the limitations of the GARCH (1, 1) model and researching asymmetry of the returns and volatility of Bitcoin, TARCH and EGARCH models were adopted; the findings indicated that the returns and volatility of Bitcoin are without a "leverage effect". To further explain this special phenomenon, safe-property is quoted in this research. In the end, this paper demonstrates that Bitcoin, as a safe-haven property, can hedge financial risks in times of economic depression. Besides, Bitcoin has a revised asymmetric effect between positive and negative shocks that makes it a viable asset to add to the portfolios of investors.</p> </abstract>

This paper investigates the extent to which volatility estimates and forecasts may be biased because of the existence of, and failure to account for structural change in the evolution of the exchange rate volatility series. The results of this analysis show that evidence of volatility persistence and long-memory in the Rand against the G4 currencies is overestimated when structural breaks are not considered. A modification of the standard GARCH model to allow for time-variation in the unconditional variance is shown to generate improved volatility forecasting performance over long(er)1 horizons for some currency pairs. Finally, the performance of the standard GARCH, modified GARCH and FIGARCH models are evaluated in the context of value-at- risk (VaR) estimation given the Basle regulatory framework. The results show that both the modified GARCH model and long-memory models generally deliver more accurate VaR measures relative to the standard GARCH model. In terms of VaR estimation our findings may provide guidance on more effective prudential standards for operational risk measurement and, as result, may help ensure adequate capitalisation and reduce the probability of financial distress. Our results highlight the importance of using out-of-sample forecasting techniques and the stipulated probability level for the identification of methods that minimise the occurrence of VaR exceptions. We find that models that account for structural change and long memory attributes generally outperform the basic GARCH model in estimating VaR across the probability levels we considered.

Developments in digital technologies are considered to be the most important innovations since the advent of the internet. In several countries, this has led to a significant change in the way payments are made, leading to new forms of payment, such as crypto-currencies. With regard to cryptocurrencies, it remains a complex issue involving especially volatility, but also money laundering and consumer protection issues. While most countries consider cryptocurrencies too volatile to be used as a payment alternative, crypto-currencies gain interest of investors in the last 10 years due to the possibility of obtaining large profits. The aim of the paper is to study the volatility of the first 5 cryptocurrencies (Bitcoin, Ethereum, Binance Coin, Cardano and Ripple) through GARCH models. The process of evaluating highly volatile cryptocurrencies is complex and depends on many parameters. Therefore, our results would be particularly useful in terms of portfolio and risk management and could help them to be more agile in evaluating their investments, in making optimal decisions and making future forecasts. We find that the GARCH (1.1) models provide the best fit, in terms of modelling of the volatility in the most popular and largest cryptocurrencies. The results show that for BTC, ETH and XRP the appropriate model is GARCH (1.1) and in the case of BNC and CARDANO GARCH-M explain better the volatility of the crypto-currencies. Therefore, more in depth analysis of the datasets may be required to confirm or deny possible structural change. The study can be complemented by carrying out an event study on the 5 cryptocurrencies analyzed or extending the analysis by applying other GARCH models, to research the optimal model for several cryptocurrencies.

Portfolio managers, option traders and market makers are all interested in volatility forecasting in order to get higher profits or less risky positions. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most popular models in modelling volatility are GARCH type models because they can account excess kurtosis and asymmetric effects of financial time series. A standard GARCH(1,1) model usually indicates high persistence in the conditional variance, which may originate from structural changes. The first objective of this paper is to develop a parsimonious neural networks (NN) model, which can capture the nonlinear relationship between past return innovations and conditional variance. Therefore, the goal is to develop a neural network with an appropriate recurrent connection in the context of nonlinear ARMA models, i.e., the Jordan neural network (JNN). The second objective of this paper is to determine if JNN outperforms the standard GARCH model. Out-of-sample forecasts of the JNN and the GARCH model will be compared to determine their predictive accuracy. The data set consists of returns of the CROBEX index daily closing prices obtained from the Zagreb Stock Exchange. The results indicate that the selected JNN(1,1,1) model has superior performances compared to the standard GARCH(1,1) model. The contribution of this paper can be seen in determining the appropriate NN that is comparable to the standard GARCH(1,1) model and its application in forecasting conditional variance of stock returns. Moreover, from the econometric perspective, NN models are used as a semi-parametric method that combines flexibility of nonparametric methods and the interpretability of parameters of parametric methods.

Volatility models based on the daily high-low range have become increasingly popular. The high and low prices are easily available, yet the range contains very useful information about volatility. It has been established in the literature that range-based volatility models outperform standard volatility models based on closing prices. However, little is known about which range-based model performs the best. We therefore evaluate two range-based volatility models, i.e. CARR and Range-GARCH with the standard GARCH model and two asymmetric GARCH models, i.e., GJR and EGARCH, based on the Monte Carlo experiments and a wide sample of currencies and stock indices. For simulated time series, the range-based models outperform the standard GARCH model and asymmetric models, and the performance of the Range-GARCH model and the CARR model is similar. However, for real financial time series (six currency pairs and nine stock indices) the Range-GARCH model outperforms the standard GARCH, GJR, EGARCH, and CARR models, while ranking of the competing models is ambiguous. We argue that Range-GARCH is the best from the competing models.

This paper investigates the volatility dynamics and underlying long memory features of four major cryptocurrencies-Bitcoin, Ethereum, Litecoin, and Ripple-which were selected due to their high liquidity, large trading volumes, and historical significance in the digital asset market. The long-range dependence exhibited in cryptocurrency markets is often overlooked. However, based on the strong evidence of persistent dependence in the return series, we adopt advanced volatility models that are capable of accommodating high volatility and heavy-tails, as well as the long memory properties of cryptocurrencies. Specifically, we employ long-memory extensions of the GAS (Long memory GAS) and GARCH (Fractionally Integrated Asymmetric Power ARCH) models, integrating heavy-tailed innovation distributions: the Generalized Hyperbolic Distribution (GHD) and Generalized Lambda Distribution (GLD). Standard GARCH and GAS models are included as benchmarks. The performance of the models are assessed using Value-at-Risk (VaR) estimation, backtesting (in-sample and out-of-sample) and volatility forecasting metrics. The results indicate that long memory models, particularly the FIAPARCH model, consistently outperforms the standard GAS and GARCH models in capturing tail risk and the volatility persistence. These findings emphasize the critical role of long memory in modeling the risk of cryptocurrencies, indicating that accounting for volatility persistence can significantly enhance the accuracy of risk estimates and strengthen risk management practices.

In this paper we compare a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the US stock market volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, in the MRS-GARCH models all parameters switch between a low and a high volatility regime. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis. The forecasting performances of the competing models are evaluated both with statistical and risk-management loss functions. Under statistical losses, we use both tests of equal predictive ability of the Diebold-Mariano-type and test of superior predictive ability. Under risk-management losses, we use a two-step selection procedure where we first check which models pass the tests of correct unconditional or conditional coverage and then we compare the best models under two subjective VaR-based loss functions. The empirical analysis demonstrates that MRS-GARCH models do really outperform all standard GARCH models in forecasting volatility at horizons shorter than one week under both statistical and VaR-based risk-management loss functions. In particular, all tests reject the presence of a better model than the MRS-GARCH with normal innovations. However, at forecast horizons longer than one week, standard asymmetric GARCH models tend to be superior.

Cryptocurrencies have rapidly emerged as a significant financial asset class, influencing global monetary systems and financial markets. However, their extreme volatility, speculative nature, and evolving regulatory landscape pose challenges to investors, policymakers, and financial analysts. This study presents an in-depth quantitative analysis of cryptocurrency volatility and risk assessment, focusing on Bitcoin (BTC-USD) and its correlation with traditional financial assets, including the EUR/USD exchange rate and S&P 500 index. Our research employs Generalized Autoregressive Conditional Heteroskedasticity (GARCH) modeling to measure the dynamic volatility patterns of Bitcoin, revealing the asset’s substantial fluctuations over time and its sensitivity to market shocks. Additionally, we utilize Monte Carlo simulations to forecast potential future price movements of Bitcoin, highlighting risk scenarios and the probability distribution of price trajectories over a one-year period. The Value-at-Risk (VaR) model is implemented to estimate potential losses within a given confidence interval, providing a robust measure of downside risk. Furthermore, the study examines the integration of cryptocurrency markets with traditional financial instruments by analyzing cross-asset correlations and volatility spillover effects. The findings suggest that while Bitcoin remains a highly volatile asset, its correlation with the broader financial system is increasing, indicating a potential shift towards mainstream financial adoption. The results contribute to the ongoing debate on whether cryptocurrencies serve primarily as speculative instruments or as viable components of diversified investment portfolios. These insights are valuable for institutional investors, risk managers, and policymakers in designing more effective risk mitigation strategies for cryptocurrency investments.

This research examines the performance of return and volatility models containing long-memory, asymmetric volatility, and leverage effects by comparing two categories of Real Estate Investment Trusts (REITs) Exchange-traded Funds (ETFs), namely, US REIT ETFs and Global REIT ETFs. This thesis utilizes two short-memory models, the autoregressive moving average – exponential generalized autoregressive conditional heteroskedasticity (ARMA-EGARCH); and autoregressive moving average – asymmetric power autoregressive conditional heteroskedasticity (ARMA-APARCH); and two long-memory models, autoregressive fractionally-integrated moving average – fractionally-integrated exponential generalized autoregressive conditional heteroskedasticity (ARFIMA-FIEGARCH); and autoregressive fractionally-integrated moving average – fractionally-integrated asymmetric power autoregressive conditional heteroskedasticity (ARFIMA-FIAPARCH). The study finds presence of volatility clustering, leverage effects and volatility asymmetry phenomena in both US and Global REIT ETFs. Also, long memory models are better in characterizing future values using lagged returns and volatilities compared to short memory models based on the maximum log-likelihood values. The research also identifies positive long-term dependence in the volatilities of both ETFs, however, fails to conclude dual long memory processes. Nevertheless, the research still can pose a challenge on the weak-form efficient market hypothesis (EMH) of Fama (1970), because historical values of REIT ETFs can still be used to predict their future values. Lastly, US REIT ETFs are seen to be more unstable than their more stationary Global REIT ETFs counterparts. The proper modeling of US and Global REIT ETFs can provide traders, fund managers and investors in creating well-defined trading strategies. Findings can also offer more understanding in the properties of this type of ETFs, and open future channels of research to academicians and researchers.

This study analyses risk-return trade-off and behaviour of various volatility dynamics including: volatility, its persistence, mean reversion and speed of mean reversion along with asymmetry and leverage effect on the Pakistani stock market by employing aggregate (aggregate market level) and disaggregate (sectoral level) monthly data for the period from 1998 to 2012. Three generalised autoregressive conditional heteroscedasticity models were applied: GARCH (1,1) for various volatility dynamics; EGARCH for asymmetric and leverage effect and GARCH-M for pricing of risk. The outcomes of the study are as follows: first, the volatility shocks are quite persistent but with varying degrees across the sectors. Both the ARCH effect (short-term effect) and GARCH effect (long-term effect) play their role in generating conditional future stock returns volatility. Further, overall the volatility process is mean reverting; however, the speed of mean reversion varies across the sectors. Secondly, the current study finds little evidence of asymmetry and leverage effect at both aggregate and disaggregates data. Thirdly, the pricing of risk (positive risk premium) is also evident, particularly at the disaggregate data in the Pakistani stock market. Finally, this research study sets the implications for both the policy makers and investors.

Value at risk (VaR) is used by financial experts to calculate and predict the risk of financial exposure. In the presence of volatility and long memory, it is a model useful for the prediction of loss in the equity index return series. Checking the accuracy of this model is necessary from the practitioners’ point of view. This article initially checks the presence of autoregressive conditional heteroscedastic (ARCH) and long-memory effects in the daily closing price of the Bombay Stock Exchange (BSE)-BANKEX return series. After confirming the ARCH and long-memory presence, it analyses the different methods of VaR calculation such as asymmetric power ARCH (APARCH), fractionally integrated exponential generalised ARCH (FIEGARCH), hyperbolic generalised GARCH (HYGARCH) and risk metrics. Then, it empirically tests the forecasting capacity of these VaR methods through techniques such as the Kupiec likelihood ratio (LR test) and dynamic quantile test. Furthermore, it checks the root-mean-squared error (RMSE) and mean absolute error (MAE) to determine the model with the least error. From the set of VaR models used here, by and large it concludes that the BANKEX return series has both long-memory and asymmetry effects. By comparing these models, it is implied that the HYGARCH model gives a better result, although the other models have their significance in the estimation and forecasting of the BANKEX return series. JEL: C12, D81, C530

This research study analyses the role of size effect in detecting the pricing of risk, various volatility dynamics, and economic exposure of firm returns on the Pakistani stock market by employing monthly data for the period from 1998 to 2018. Three generalized autoregressive conditional heteroskedasticity models were applied: GARCH(1,1) for capturing different volatility dynamics, GARCH-M for pricing of risk, and EGARCH for asymmetric and leverage effect. The findings of the study are as follows: Firstly, the authors untie that pricing of risk is subject to considerable variations with respect to firm size. Secondly, in the process of detecting whether the firm size matters in the case of asymmetry and leverage effect, they find that it is indeed the case. Thirdly, size effect plays a substantial role in determining various volatility dynamics. Finally, they uncover that economic factors affect stock returns differently based on firm size, signifying the role of size effect.

This paper is concerned with the behavior of energy ETF prices. It applies three models: autoregressive moving average (ARMA) and generalized autoregressive conditional heteroskedasticity (GARCH), along with their revised forms, ARMA–Exponential-GARCH, Glosten-Jagannathan-Runkle (GJR), and GARCH diffusion process with jump models. This study looks at the volatility behavior and jumps dynamics of Energy and Master Limited Partnership's (MLP) ETFs. The results show that ARMA-GARCH is appropriate for modeling energy and MLP ETFs. Both ETFs offer positive leverage and asymmetric volatility. The results show that the jump model with a GARCH volatility specification has an actual amount of jump presence and time variation in the jump size distribution. The conclusion of the ARMA - EGARCH model gives evidence of the reverse leverage effect. The leverage term positively influences the conditional variance, while the asymmetry coefficient for the GJR model is positive and significant. These results reveal that both Energy and MLPs ETF have high volatility. JEL classification numbers: F3. Keywords: Energy ETFs, MLPs, ARMA-GARCH model, Volatility Asymmetry, Leverage and Jump Effect.