In this chapter of our study, we highlight the methodological findings as well as the main conclusions of the literature concerning volatility and risk management in cryptocurrencies.
4.1. Methodological Findings
The comparison of econometric models used for cryptocurrency’s volatility is addressed in studies such as
Hattori (
2020) which evaluates the volatility modelling in the Bitcoin market considering realized volatility, and models such as the GARCH, GJR-GARCH, EGARCH, APARCH, and IGARCH, using their error terms modified by normal, t and skewed t distributions. Extant literature has used extensively these models to analyze cryptocurrencies markets (e.g.,
Vidal-Tomás and Ibañez 2018).
The MSE and the QLIKE loss functions with the RV, are also considered, as volatility proxy. The results reveal that compared with the other models the EGARCH and the APARCH are highly ranked, and that they perform better with the normal distribution. If we consider QLIKE, the EGARCH with normal distribution has the best predictability, however, if we consider MSE, the APARCH with normal distribution is the best predictor model. The author concludes that concerning the Bitcoin data, the normal distribution is the better fit, and that the EGARCH and the APARCH models have the highest predictive power.
On the other hand,
Peng et al. (
2018) in a study to examine cryptocurrencies’ volatility predictive performance, shows evidence that compared to GARCH, EGARCH, and GJR-GARCH models with student-t, skewed student-t, and even with normal distributions, the SVR-GARCH model outperforms its benchmarks for all variables and time frames. Furthermore, according to
Acereda et al. (
2020), who examined the importance of conditional variance and error distribution in the parametric models when estimating the Expected Shortfall (ES) of cryptocurrency returns. It is crucial to estimate the Expected Shortfall (ES) of Bitcoin return series using a non-normal error distribution with two parameters and the NGARCH or the CGARCH models. For other cryptocurrencies, the results are not clear. However, the authors indicate that the heavy-tailed distribution produces better results than the normal distribution.
Additionally, in the study conducted by
Wang et al. (
2019), who used realized volatility from high-frequency data to evaluate ARJI, GARCH, EGARCH, and CGARCH models’ performance, it is shown that the ARJI model, which is a model that allows for jump dynamics, in comparison to the other models under study, reveals to be the ideal model to predict Bitcoin’s price volatility dynamics. The model also reveals superior sample goodness of fit, as well as out-of-sample predictive performance, compared to the other models. The authors also indicate that through the MZ regression, the GARCH-type models explain about 15% of the latent Bitcoin price volatility.
In another study,
Aras (
2021) investigated the different hybrid GARCH models that forecast performance using machine learning techniques. The author opted to use as models, the support vector machines (SVM) model, the artificial neural networks (ANN) model, the random forest (RF) model, and the K-nearest neighbors (KNN) model. The author also considered the GARCH (2,2) model, and a stacking assemble methodology. LASSO was chosen as the feature selection technique, and as the feature extraction technique PCA is used. The results indicate that the stacking assemble methodology with LASSO outperforms the base models, and therefore it can be reached better volatility forecasts than in those hybrid GARCH models often used in the literature. Furthermore, the best hybrid model performances are related to the models that consider the SVM.
On the other hand,
Köchling et al. (
2020), to better forecast Bitcoin’s volatility using GARCH-type models, applied different volatility proxies and loss functions. In their study, the authors highlight that through a model confidence set (MCS), the ARCH (1) and IGARCH (1,2) are the more promising models. However, the ARCH (1) model forecasts seem to be stable, whereas the IGARCH (1,2) model forecasts vary. In this sense, through the fact that a simple ARCH (1) model performs comparatively well, the authors conclude that the Bitcoin dynamics can be hard to predict even in sophisticated models.
Several studies apply a Markov-switching regime model such as
Maciel (
2021) that compares the performance of prediction on MS-GARCH against traditional single-regime GARCH methods for volatility forecasts. The results indicate that there are regime changes in daily log-returns’ volatility, with low and high regimes. Furthermore, when skewed distributions are considered, and when the scedastic function takes into consideration the leverage effects, the MS-GARCH models are better specified. Finally, compared with the standard single-regime GARCH models, and according to the economic criterion (VaR and ES) the MS-GARCH model is more accurate in predicting the short-, medium- and long-term horizons. Therefore, Markov-switching volatility models can help cryptoinvestors.
In the same line,
Tan et al. (
2021) considered tree GRACH model specifications such as the GARCH (1,1) model; the GJR-GARCH (1,1) model, where there is a degree of asymmetry effect that corresponds to the past shock in the conditional variance; and the TGARCH (1,1) model, that takes into account the leverage effect. In order to enable dynamic parameters, the authors also considered the MS-GARCH (1,1) model, allowing to analyse the regime change impact on volatility and mean levels. Allowing more flexibility, they also adopted the TVTP specification resulting in a TV-MS-GARCH (1,1) model. The results revealed improving performances for Bitcoin volatility forecasting by the TV-MS-GARCH (1,1) model with the skewed and fat tail error distributions, outperforming the other models. Furthermore, the authors highlight that it is crucial to incorporate exogenous variables into the TV-MS-GARCH model.
Mba and Mwambi (
2020) present a two-state Markov-switching COGARCH-R-vine (MS-COGARCH) model for cryptocurrencies portfolio selection and compare its performance to the single-regime COGARCH-R-vine (COGARCH). The authors use the vine copula models that overcome the problem of lack of flexibility of multivariate copulas, by using bivariate conditional copulas as a building block, therefore making these models more flexible in caching the underlying dependence and tail dependence structure. The results reveal that the single-regime optimal portfolio presents a higher level of risk compared to the Markov-switching. Furthermore, the Markov-switching has a greater ability to model cryptocurrencies volatility and portfolio risk. However, it has little influence on the returns of a cryptocurrency portfolio. The authors conclude that the MS-COGARCH outperforms the single-regime COGARCH. Additionally, the flexibility of the R-vine copula allows a proper bivariate copula selection for each pair of cryptocurrencies in order to have a proper dependence structure through pair-copula construction architecture.
These results are in line with the research conducted by
Caporale and Zekokh (
2019) who investigated the best methodology to model cryptocurrencies’ volatility (Bitcoin, Ethereum, Ripple, and Litecoin) between 2010 and 2018. The authors considered the MS-GRACH, SGARCH, EGARCH, GJR-GARCH, and the TGARCH models, to estimate one step ahead prediction of VaR and ES through a rolling window analysis. To choose the best models, the authors used the model confidence set (MCS), which is a sequential test that removes the worst model in each step and builds a “set of superior models” (SSM), where the hypothesis of equal predictive ability is not rejected. The authors tested more than 1176 GARCH-type models for each cryptocurrency, with a maximum likelihood procedure. The results indicate that VaR and ES better predictions are made by the two-regime GRACH. Therefore, the authors concluded that incorrect Value-at-Risk (VaR) and Expected Shortfall (ES) predictions can be presented by using standard GARCH models, which leads to ineffective portfolio optimization and risk management. However, to improve this, the authors suggest the use of model specifications that allow for asymmetries and regime-switching. In the same line,
Ma et al. (
2020) also gave a contribution through their research by proposing a novel Markov regime-switching mixed data sampling (MRS-MIADS) model in order to improve the accuracy prediction of Bitcoins’ realized variance (RV). The authors compared the various types of models, which indicated that the TVTP-MRS-MIDAS-CJL model exhibits a significant improvement for two weeks and one-month horizons. However, the FTP-MRS-MIDAS-CJL model presents better forecasting performance for 5 days and 66 days horizons. Moreover, the TVTP-MRS-MIDAS-CJL model reveals that jumps have different predictive power for Bitcoin’s RV, showing high and low volatility regimes.
Similar to
Ma et al. (
2020), there are also other studies that employ novel models, such as the one conducted by
Mba et al. (
2018) who proposed as new approaches the GARCH-differential evolution (GARCH-DE) and the GARCH-differential evolution t-copula (GARCH-DE-t-copula). The traditional differential evolution (DE) is contrasted with those new models in a single and multiperiod optimization, under the coherent risk measure CVaR constraint. The authors also use t-copula due to its ability to better capture the dependency of fat tails displayed by financial data. Under the single period optimization analysis, the authors found that the GARCH-DE-t-copula outperforms the GARCH-DE in terms of returns and as well as risk control. Under the multiperiod optimizations analysis, the GARCH-DE-t-copula outperforms both the DE and the GARCH-DE, having the highest returns. Therefore, the authors highlight that in portfolio optimization the DE power increases when combined with t-copula.
Phillip et al. (
2019) argue that cryptocurrencies require specific modelling, since they present challenges that fiat currencies do not. Therefore, they opted to analyze cryptocurrencies’ volatility using a novel model. First, and in order to account for occasional jumps, the authors selected the Buffered Autoregressive (BAR) model. Then, to use long-run autocorrelation with structural changes, they added the time-varying SV model. Due to the oscillatory behavior of cryptocurrencies, the authors also incorporated the Gegenbauer long-run autocorrelation filter. Therefore, the authors used a Jump BAR SV Gegenbauer Log Range (JBAR-SV-GLR) model. The results reveal that oscillatory long run autocorrelations are better filters to model the log daily return range instead of the standard long run autocorrelations. Consequently, the authors state that cryptocurrencies’ volatility can be better analyzed through fast moving autocorrelation functions, instead of smoothly decaying functions used for fiat currencies.
Finally, there are also other studies such as the one conducted by
Cheikh et al. (
2020) that used a Smooth Transition GARCH (ST-GARCH) model to investigate the presence of asymmetric volatility dynamics in Bitcoin, Ethereum, Ripple, and Litecoin. By choosing the ST-GARCH model, the authors allow for continuum intermediate states between two extreme volatility regimes. For comparison purposes, the authors also used other models along with the ST-GARCH model, such as the standard GARCH model, exponential GARCH (EGARCH) model, threshold GJR-GARCH model, and the threshold GARCH (ZARCH) model. The results reveal through the log-likelihood values that the ST-GARCH provides the best fit for Bitcoin, Ripple, and Litecoin. However, according to the AIC and BIC information criteria, Ethereum is the only exception where the ZARCH model has a better specification than the ST-GARCH model.
In a study conducted by
Ftiti et al. (
2021), they examine the modelling and forecasting of volatility in the cryptocurrency market, based on high-frequency data, with special regard for periods of crisis. The authors opted to consider an intraday volatility measure of the RV. They then decompose the RV into continuous and discontinuous components, and into positive and negative semi-variances. The paper also decomposed the realized semi-variance into continuous and jump components. They use five models to forecast volatility, namely the HAR-RV model, as the benchmark model, since it considers the investors’ heterogeneity; the HAR-CV-J model, in which the continuous and the discontinuous components are used to replace the RV; the HAR-SRV model, which considers the decomposition of positive and negative volatility; the HAR-RV-ΔJ2 model, which analyses the effect of a signed jump; and the HAR-RV- ΔJ2+-ΔJ2- model, which is an extension of the previous models. The model confidence set (MCS) method was used to evaluate the best model. The findings reveal that in either crisis or non-crisis periods, the best model for predicting future volatility seems to be an extended HAR model that includes positive and negative semi-variances.
Regarding future indications or improvements on the methodologies used, the authors indicate that the heterogeneous autoregressive regression (HAR) model is better suited to improve Bitcoin’s realized volatility prediction, and, thus, it should be considered in future research (
Hattori 2020). Furthermore, the great variety of GARCH models should be further explored from the staking ensemble perspective (
Aras 2021), and that it would be interesting to further explore the linkages between Bitcoin and other altcoins through multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models (
Caporale and Zekokh 2019).
There are also indications for future works to compare the Markov-switching GARCH (MS-GARCH) models to other volatility methods based on realized variance, as well as to consider conditional’s variance long memory property when conducting a cryptocurrencies’ volatility forecast (
Maciel 2021). It is also highlighted the need to adopt heterogeneous autoregressive regression—mixed data sampling (HAR-MIDAS) model and use intraday data to build daily realized volatility measures (
Walther et al. 2019), as well as the inclusion of Support Vector Regression (SVR) estimation in order to improve volatility’s predictions (
Peng et al. 2018).
Through the summary of the models proposed to model cryptocurrency volatility, presented in
Table 6, we evidence that though, there are indications of many models that show a good performance to measure and forecast cryptocurrencies’ volatility, the models that consider the Markov-switching regime seem to be more consensual. Regarding machine learning techniques the best hybrid model performances are related to the models that consider the SVM.
4.2. Discussion of Main Findings
In the review of the studies, we identify evidence that Bitcoin in some cases can be considered a hedge, and in others can be considered a diversifier. Specifically, against the Euro-Index, Shanghai A-Share, S&P 500, Nikkei, and the TSX Index, considering monthly returns, Bitcoin can be used as a strong hedge (
Chan et al. 2019). The same cannot be said if we consider weekly returns. Thus, evidencing the fact that in these cases investors may have hedging benefits from holding Bitcoin longer (
Chan et al. 2019). However, under extreme market conditions, the role of Bitcoin might change from hedge to diversifier (
Garcia-Jorcano and Benito 2020). The benefits of Bitcoin diversification can be found if we consider it in a commodities portfolio. There are also diversification benefits from intraweek and monthly scales for BitShares, Litecoin, Stellar, Ripple, Monero, and DASH (
Omane-Adjepong and Alagidede 2019). Nonetheless, if investors consider many economic instruments in their portfolios, the inclusion of Bitcoin is off reduced benefits (
Symitsi and Chalvatzis 2019).
There is also evidence that Bitcoin and precious metals share an asymmetric response in the same direction to market shocks. However, unlike gold, the case of Bitcoin shows a positive coupling effect, which in situations of shocks and market decline, means that Bitcoin also declines (
Klein et al. 2018).
Regarding spillovers between cryptocurrencies and other markets as well as amongst the cryptocurrency market, evidence shows returns and shocks spillovers between the Bitcoin market and stock markets. This implies that rational investors move across markets as a strategy to manage their portfolios in order to prevent the “crystallization” of shocks to their portfolios’ value (
Uzonwanne 2021). There is also evidence that, in their pursuit for a hedge in the equity market, investors transmit uncertainty and volatility to the cryptocurrency market (
Cheikh et al. 2020). On the other hand, considering not only Bitcoin but also other cryptocurrencies there is evidence that a spillover effect of an initial shock in the cryptocurrency market is felt by the financial markets. However, the high-yield hedged bond and equity markets show persistence in the subsequent volatility spillovers originating in the cryptocurrency market (
Omane-Adjepong and Alagidede 2019). Nonetheless, their levels of connection and volatility linkages are sensitive to trading scales (
Omane-Adjepong and Alagidede 2019). There is also evidence of spillovers between cryptocurrencies, specifically bidirectional volatility spillover effects, between Bitcoin and Ethereum, between Bitcoin and Litecoin, and between Ethereum and Litecoin. Thus, supporting the idea of an integrated cryptomarket (
Katsiampa et al. 2019).
Regarding news effects, evidence shows that good news has more impact than bad news on cryptocurrency’s volatility. This asymmetric effect is a feature of assets that can suit as a safe haven (such as Gold) (
Baur and Dimpfl 2018;
Cheikh et al. 2020). In this regard, it is more likely that optimistic investors buy when the news is good than pessimistic investors sell when the news is bad (
Sapuric et al. 2020). Bad news volatility during crisis periods, means that cryptocurrency investors are stressed and overreact to negative news (
Ftiti et al. 2021). In this way, due to the “fear of missing out” (FOMO) by uninformed investors on high cryptocurrency valuations, the volatility response to positive shocks increases. On the other hand, the behavior of informed investors explains the negative shocks’ asymmetric volatility response (
Baur and Dimpfl 2018). Despite being considered an alternative asset class, cryptocurrencies are leading investors’ sentiment in the financial markets (
Umar et al. 2021).
Regarding volatility predictability in the cryptomarket, evidence points out that exogenous variables such as the Global Real Economic Activity, Global Financial Stress Index, and Chinese Policy Uncertainty Index, contain useful information for cryptocurrencies’ volatility forecast. Thus, emphasizing that there is a network of factors that interact with each other, instead of a single factor (
Walther et al. 2019).
There is also evidence that options may play a significant role for Bitcoin investors, providing important information (
Hoang and Baur 2020). In this way, results show that for one percentual point change in the implied volatility, the premium seems to show increasing sensitivity and that in different expirations dates for a one percentual point change in the risk-free rate the premium remains largely stable (
Jalan et al. 2021). Regarding longer maturities, the prices of Bitcoin options seem to be less sensitive to changes in the value of the underlying (Bitcoin) (
Jalan et al. 2021). Finally, Bitcoin, Ethereum, and Ripple volatilities can be used for trend-trending strategies. For instance, a straddle trading strategy that implements Bitcoins’ long position volatility by the purchase of a Bitcoin put option and a Bitcoin call option with the same expiration and strike (
Siu 2021).
Regarding cryptocurrencies as a medium of exchange, evidence indicates that the ones that are faster transacted are preferable because of their lower liquidity risk (
Phillip et al. 2019). It also found a connection between the number of new crypto accepting venues and volatility. In this way, cryptocurrency volatility decreases when firms withdraw crypto payment options and increases when firms introduce these crypto payment options. Thus, the number of new venues that accept cryptocurrencies as a form of payment can predict cryptocurrency volatility (
Sabah 2020).
It can also be learned from the analysis of studies accommodated in our review that between the years 2014 and 2017, both Litecoin and Bitcoin were more volatile than the Euro (
Miglietti et al. 2020). Furthermore, the oldest, least volatile, and most persistent coins are Bitcoin and Litecoin, and on the other hand, Ethereum presents a moderate level of volatility and persistence, and Ripple presents zero leverage strong autoregression (
Tan et al. 2020). There is also evidence of positive and significant relationships between volume and returns before the Mt. Gox hack, as well as between volume and volatility after the year 2013 (
Sapuric et al. 2020). The predictability of volatility, risk reduction, and level of speculation in the cryptocurrency market is improved by the leverage effects and the volatility persistence (
Tan et al. 2020).
As far as future avenues of research are concerned, we find indications for a reanalysis of Bitcoin’s ability to be a hedge against equity investments, in more mature cryptocurrency markets (
Klein et al. 2018), and also a reanalysis of the relationships between Bitcoin’s returns, volatility, and volume, since the relationships between these variables may change over time (
Sapuric et al. 2020). Additionally, it is encouraged the construction of portfolio optimization strategies since cryptocurrency investors stress and overreact to negative news during periods of crises (
Ftiti et al. 2021). It is also encouraged to understand cryptocurrencies’ returns and volatility spillovers magnitude, in normal as well as in crisis periods (
Umar et al. 2021), and to quantify leading shock transmitters, or receivers, for the cryptocurrency markets, regarding different time horizons (
Omane-Adjepong and Alagidede 2019). As well as to analyze the volatility dynamics concerning cryptocurrencies’ market speculation (
Tan et al. 2021) and a multi-regime analysis concerning dynamic changes in Bitcoin prices (
Tan et al. 2021).
Additionally, it is argued the need to explore the behavioral anomalies and market efficiency or inefficiency impacts on cryptocurrencies risk and portfolio allocation, using acceptability indexes and market cones (
Siu 2021), as well as the need for further analysis on the stylized facts of cryptocurrencies, such as the leverage effect (
Phillip et al. 2019) and their behavior during the COVID-19 pandemic (
Garcia-Jorcano and Benito 2020). Moreover, there is the need to study if cryptocurrency realized volatility or its trading volume drives the long-term volatility, and to examine the add-value of exogenous drivers in trading strategies, portfolio allocation, and risk management (
Walther et al. 2019).
Finally, we point to the importance of further comparing volatility prediction of Bitcoin’s call and put option returns to the commodity options (
Jalan et al. 2021), and to analyze the influence of options trading on the volatility of cryptocurrencies, as well as to understand whether investors prefer an unregulated exchange over a regulated one (
Hoang and Baur 2020).