This study investigates the scale-dependent structure of asymmetric volatility effect in six representative cryptocurrencies: Bitcoin, Ethereum, Ripple, Litecoin, Monero, and Dash. By developing the dynamical approach of DFA-based fractal regression analysis, we detect whether the volatility of price changes is positively or negatively related to return shocks at different time scales. We find that the asymmetric volatility phenomenon varies by scale and cryptocurrency, and the structure is time-varying. Contrary to what is typically observed in equity markets, minor currencies show an “inverse” asymmetric volatility effect at relatively large scales, where positive shocks (good news) have a greater impact on volatility than negative shocks (bad news). The consequences are discussed in the context of who is trading in the market and heterogeneity of the investors.
The cryptocurrency market offers significant investment opportunities but also entails higher risks as compared to other asset classes. This article aims to analyse the financial risk characteristics of individual cryptocurrencies and of a broad cryptocurrency market portfolio. We construct a portfolio comprising the 20 largest cryptocurrencies, which cover 82.1% of the total cryptocurrency market. The returns are examined for extreme tail risks by the application of Extreme Value Theory. We utilise the GARCH-EVT approach in combination with a novel algorithm to automatically determine the optimal threshold to model the tail distribution. Furthermore, we aggregate the individual market risks with a t-Student Copula to investigate possible diversification effects on a portfolio level. The empirical analysis indicates that all examined cryptocurrencies show high volatility in their price movements, whereby Bitcoin acts as the most stable cryptocurrency. All return distributions are heavy-tailed and subject to extreme tail risks. We find strong, positive intra-market correlations, in particular with the two largest cryptocurrencies Bitcoin and Ethereum. No diversification effect can be achieved by aggregating market risks. On the contrary, a negligibly lower expected return and higher joint extreme returns can be observed. From this analysis, it can be concluded that investments in individual cryptocurrencies as well as in a portfolio show extreme risks of losses. From the investor’s point of view, a possible strategy of risk reduction through portfolio formation within cryptocurrencies is only promising to a limited extent and does not offer a satisfactory solution to significantly reduce the risk within this asset class.
Çalışmanın temel amacı bitcoin ile BIST30 vadeli, altın vadeli ve döviz vadeli işlemler piyasası arasındaki volatilite etkileşimini araştırmaktır. Bu doğrultuda 25.07.2010 – 13.02.2022 dönemine ait haftalık veriler kullanılmıştır. Bitcoin ile BIST30 vadeli, altın vadeli ve döviz vadeli işlemler piyasası arasındaki volatilite etkileşimini araştırmak için çok değişkenli GARCH modellerinden DCC-GARCH modeli kullanılmıştır. Bitcoin, BIST30 vadeli, altın vadeli ve döviz vadeli işlemler piyasasında meydana gelen volatilitenin kalıcı olduğu tespit edilmiştir. Bitcoin ile BIST30 vadeli işlemler piyasası arasında çift yönlü, altın ve döviz vadeli işlemler piyasasında bitcoin’e doğru tek yönlü volatilite etkileşimi bulunmaktadır. Bitcoin ve BIST30 vadeli işlemler piyasası, altın vadeli işlemler piyasasından bitcoine doğru negatif yönlü etkileşim mevcuttur. Fakat döviz vadeli işlemler piyasasından bitcoine doğru volatilite etkileşimi ise pozitif yönde olduğu saptanmıştır.
Bitcoin derivatives positions are maintained with a self-selected margin, which is often too low to avoid automatic liquidation by the exchange, without notice, especially during periods of excessive volatility. Indeed, according to CryptoQuant, almost $80 billion of positions on centralised exchanges were liquidated during 2021, that is an average of over $200 million per day. So hedgers of bitcoin price risk should account for the possibility of automatic liquidation when taking positions on bitcoin futures. We derive a semi-closed form for an optimal hedging strategy with dual objectives – to minimize both the variance of the hedged portfolio and the probability of liquidation due to insufficient collateral. The solution depends on the statistical characteristics of the spot and futures extreme returns, and other parameters that characterize the hedger by choice of leverage, loss aversion and collateral management. An empirical analysis based on minute-level data compares the performance of the major direct and inverse bitcoin hedging instruments traded on five major exchanges.
This paper attempts to understand the dynamic interrelationships and financial asset capabilities of Bitcoin by analysing several aspects of its volatility vis-a-vis other asset classes. This study aims to analyse the volatility dynamics of the returns of Bitcoin. An asymmetric GARCH model (EGARCH) is used to investigate whether Bitcoin may be useful in risk management and ideal for risk-averse investors in anticipation of negative shocks to the market (leverage effect). This paper also examines Bitcoin as an investment and hedge alternative to gold as well as NSE NIFTY using a multivariate DCC GARCH model. DCC GARCH models are also used to check whether correlation (co-movement) between the markets is time-varying, examine returns and volatility spillovers between markets and the effect of the outbreak of COVID-19 in India on the investigated markets. The results show that given the supply of Bitcoin is fixed, low returns realisation is equivalent to excess supply over demand wherein investors are selling off Bitcoin during bad times. The positive co-movement between Bitcoin and gold during the COVID-19 outbreak shows that investors perceived Bitcoin as a relatively safe investment. However, overall analysis shows that Bitcoin was not considered a safe hedge and an investment option by Indian investors during the study period.
Marcin Wątorek, Jarosław Kwapień, Stanisław Drożdż
Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a subject of systematic study. In order to fill this gap, we analyse detrended correlations of the price returns, the average number of trades in time unit, and the traded volume based on high-frequency data representing two major cryptocurrencies: bitcoin and ether. We apply the multifractal detrended cross-correlation analysis, which is considered the most reliable method for identifying nonlinear correlations in time series. We find that all the quantities considered in our study show an unambiguous multifractal structure from both the univariate (auto-correlation) and bivariate (cross-correlation) perspectives. We looked at the bitcoin--ether cross-correlations in simultaneously recorded signals, as well as in time-lagged signals, in which a time series for one of the cryptocurrencies is shifted with respect to the other. Such a shift suppresses the cross-correlations partially for short time scales, but does not remove them completely. We did not observe any qualitative asymmetry in the results for the two choices of a leading asset. The cross-correlations for the simultaneous and lagged time series became the same in magnitude for the sufficiently long scales.
This research assesses the diversification patterns for tail dependence between Bitcoin return and trading volume by utilizing a dynamic mixture copula approach with spillover effect and asymmetric volatility effect. There are four main empirical findings. First, the spillover effect between return and trading volume exists. Second, the leverage effect is statistically significant for return and trading volume. Third, the linkages between return and trading volume are diversified. Both positive and negative tail dependence structures are observed, and the frequency of a positive tail dependence occurring is higher. Furthermore, the asymmetric tail dependence structure exists in positive and negative dependence situations. In the positive dependence structure, a co-movement in the increasing direction is stronger than a co-movement in the decreasing direction. In the negative dependence structure, a situation of a large return with low volume occurs more often than a situation of a small return with high volume. Fourth, the volatility of trading volume positively predicts the magnitude of positive dependence.
Over the past years, cryptocurrencies have drawn substantial attention from the media while attracting many investors. Since then, cryptocurrency prices have experienced high fluctuations. In this paper, we forecast the high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling volatility to select the best model. We propose various generalized autoregressive conditional heteroscedasticity (GARCH) family models, including an sGARCH(1,1), GJR-GARCH(1,1), TGARCH(1,1), EGARCH(1,1), which we compare to a multivariate DCC-GARCH(1,1) model to forecast the intraday price volatility. We evaluate the results under the MSE and MAE loss functions. Statistical analyses demonstrate that the univariate GJR-GARCH model (1,1) shows a superior predictive accuracy at all horizons, followed closely by the TGARCH(1,1), which are the best models for modeling the volatility process on out-of-sample data and have more accurately indicated the asymmetric incidence of shocks in the cryptocurrency market. The study determines evidence of bidirectional shock transmission effects between the cryptocurrency pairs. Hence, the multivariate DCC-GARCH model can identify the cryptocurrency market’s cross-market volatility shocks and volatility transmissions. In addition, we introduce a comparison of the models using the improvement rate (IR) metric for comparing models. As a result, we compare the different forecasting models to the chosen benchmarking model to confirm the improvement trends for the model’s predictions.
Mnacho Echenim, Emmanuel Gobet, Anne-Claire Maurice
We design a novel calibration procedure that is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. We show that this calibration procedure is significantly more robust and accurate than the standard one based on trade and mid-prices.
Objective: The purpose of this paper is to demonstrate the effectiveness of the nonparametric GARCH model for the prediction of future Bitcoin prices. Methodology: The parametric GARCH models to characterize the volatility of Bitcoin returns are widely used in the empirical literature. Alternatively, we consider a non-parametric approach to model and forecast the volatility of Bitcoin returns. Results: We show that the volatility forecast of the nonparametric GARCH model yields superior performance compared to an extended class of parametric GARCH models. Originality / relevance: The improved accuracy of forecasting the volatility of Bitcoin returns based on the nonparametric GARCH model suggests that this method offers an attractive and viable alternative to commonly used GARCH parametric models.
Blockchain and cryptocurrency are gradually going mainstream with new cryptocurrencies introduced every single day. The speculative nature of these digital assets expose their prices to large fluctuations. Trading these crypto-assets necessitate an adequate understanding of this emerging market as well as adequate tools to model the market risk and efficient allocation of funds. This may assist crypto investors in taking advantage of the highly volatile aspects of these assets. The portfolio consider in this study consists of six cryptocurrencies: four traditional cryptocurrencies (BTC, ETH, BNB and XRP) and two stablecoins (USDT and USDC). We examine the copula particle swarm optimization (CPSO) portfolio strategy against three other portfolio strategies, namely, the global minimum variance (GMV), the most diversified portfolio (MDP) and the minimum tail dependent (MTD). CPSO appears to be a promising strategy during extreme market conditions while GMV seem favorable during normal market conditions. Most importantly, hedge and safe-havens ability of the two stablecoins is clearly exhibited with CPSO, while their diversification property is inhibited.
H. M. Tenkam, Jules C. Mba, Sutene Mwambetania Mwambi
This paper focuses on the selection and optimisation of a cryptoasset portfolio, using the K-means clustering algorithm and GARCH C-Vine copula model combined with the differential evolution algorithm. This integrated approach allows the construction of a diversified portfolio of eight cryptocurrencies and determines an optimal allocation strategy making it possible to minimize the conditional value-at-risk of the portfolio and maximise the return. Our results show that stablecoins such as True-USD are negatively correlated to the other cryptoassets in the portfolio and could therefore be a safe haven for crypto-investors during market turmoil. Our findings are in line with previous studies exhibiting stablecoins as potential diversifiers.
Kwapie\'n, Jaros{\l}aw, W\k{a}torek, Marcin, Marija Bezbradica, Martin Crane · 6 authors
We analyse tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra $f(\alpha)$ indicating that the periods of increased market activity are characterised by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution are able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former, some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observation is that parallel data sets from different trading platforms can show disparate statistical properties.
The objective of this study is to use the South African financial markets (Johannesburg Stock Exchange or JSE and USD/ZAR) as a case study to understand the volatility spillover dynamics of Bitcoin as a digital asset. Methodologically, the study applies the exponential generalized autoregressive conditional heteroskedastic (EGARCH) model, followed by a robustness check by applying the time-varying conditional correlation multivariate GARCH (VCC-MGARCH) model. The study utilizes the data set for the period 2011 to 2019, a period before the COVID‑19 pandemic. The research outcome revealed three interesting observations. First, Bitcoin and the South African stock market are independent of each other. Second, there is a bidirectional shock transmission between Bitcoin and USD/ZAR in the mean returns only, but not variance. Lastly, results confirm the existence of a bidirectional volatility spillover in both the mean and variance between the JSE stock market and the USD/ZAR market. The study outcome should enlighten investors who may want to consider Bitcoin as a diversifier in their investment and portfolio strategies.
This paper aims to investigate and measure Bitcoin and the five largest stablecoin market volatilities by incorporating various range-based volatility estimators to the BEKK- GARCH and Copula-DCC-GARCH models. Specifically, we further measure Bitcoins’ volatility related to five major stablecoins and examine the connectedness between Bitcoin and the stablecoins. Our empirical findings document that the connectedness between Bitcoin and stablecoin market volatility behaviors exhibits the presence of stable interconnection. This study is of particular importance since it is crucial for market participation in the ongoing crypto assets to be informed about both the volatility patterns of major cryptocurrencies and the relative volatility of Bitcoin against the stablecoin markets. Eventually, we find that there is no systematic evidence for the various parity deviations of the stablecoins that are profoundly impacted by Bitcoin volatility. Thus, Bitcoin and the largest stablecoin Tether could stabilize together. However, Bitcoin shall not be generalized to other stablecoins in terms of stability results.
This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model. Supplementary Information: The online version contains supplementary material available at 10.1007/s00181-022-02255-z.
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 the continuous-time GARCH model shows a better performance to predict the volatility.