This paper aims to select the best model or set of models for modelling volatility of the four most popular cryptocurrencies, i.e. Bitcoin, Ethereum, Ripple and Litecoin. More than 1000 GARCH models are fitted to the log returns of the exchange rates of each of these cryptocurrencies to estimate a one-step ahead prediction of Value-at-Risk (VaR) and Expected Shortfall (ES) on a rolling window basis. The best model or superior set of models is then chosen by backtesting VaR and ES as well as using a Model Confidence Set (MCS) procedure for their loss functions. The results imply that using standard GARCH models may yield incorrect VaR and ES predictions, and hence result in ineffective risk-management, portfolio optimisation, pricing of derivative securities etc. These could be improved by using instead the model specifications allowing for asymmetries and regime switching suggested by our analysis, from which both investors and regulators can benefit.
This paper aims to elucidate the connectedness between major forex currencies and cryptocurrencies using the quantile cross-spectral approach recently proposed by Baruník and Kley (2015). The sample covers six forex currencies and six cryptocurrencies over the period of 1 September 2015 to 29 December 2017. Compared with the results obtained from standard correlations and detrended moving-average cross-correlation analysis (DMCA), the quantile cross-spectral approach provides richer information on the dependence structure across different quantiles and frequencies. The most interesting result is that the intra-group dependencies are positive in the lower extreme quantiles, while inter-group dependencies are negative. This result holds in both the short- and long-term perspectives. Thus, it is worth diversifying between these two currency groups.
Cryptocurrencies such as Bitcoin are establishing themselves as an investment asset and are often named the New Gold. This study, however, shows that the two assets could barely be more di?erent. Firstly, we analyze and compare conditional variance properties of Bitcoin and Gold as well as other assets and ?nd di?erences in their structure. Secondly, we implement a BEKK-GARCH model to estimate time-varying conditional correlations. Gold plays an important role in ?nancial markets with ?ight-to-quality in times of market distress. Our results show that Bitcoin behaves as the exact opposite and it positively correlates with downward markets. Lastly, we analyze the properties of Bitcoin as portfolio component and ?nd no evidence for hedging capabilities. We conclude that Bitcoin and Gold feature fundamentally di?erent properties as assets and linkages to equity markets. Our results hold for the broad cryptocurrency index CRIX. As of now, Bitcoin does not re?ect any distinctive properties of Gold other than asymmetric response in variance.
This paper examines the movement of cryptocurrencies’ return based on price. This volatility can spread to others of the same kind. Currently, the more cryptocurrencies are traded in market, the more chances are available for investors. The author wonders whether contagion risk among these cryptocurrencies happens or not in the event of crashing. We also introduce one empirical evidence of the mutual influence on these cryptocurrencies using Copulas approach. The findings show that all pairs have the structure dependence with Kendall-plots, particularly strong left tail dependence with Chi-plots. It also means the existence of contagion risk among these cryptocurrencies. The three methodologies namely Kendall-plots, Chi-plots and Copulas estimation produce consistent results. Therefore, the investors should carefully perform portfolio diversification to avoid contagious phenomenon.
The emergence of Bitcoin in 2009 has received considerable attention surrounding the validity of cryptocurrencies as a viable and, in some jurisdictions, a legal currency alternative. Despite widespread concern that these cryptocurrencies are fostering the environment within which a substantial bubble can occur, it is important to analyze whether these new assets are behaving similarly to major international currencies. This paper investigates the effects of international monetary policy changes on bitcoin returns using a GARCH (1.1) estimation model. The results indicate that monetary policy decisions based on interest rates taken by the Federal Open Market Committee in the United States significantly impact upon bitcoin returns. After controlling for international effects, we find significant evidence of volatility effects driven by United States, European Union, United Kingdom and Japanese quantitative easing announcements. These results show that, despite its nature and ideals, bitcoin seems to be subject to the same economic factors as traditional fiat currencies, and is not entirely unaffected by government policies. This result has implications for investors using bitcoin as a hedging or diversification tool. In addition, we contribute to the existing debate regarding the classification of bitcoin as an asset class, by illustrating that bitcoin volatility exhibits various reactions that bear resemblance to both currency pairs and store-of-value assets.
The 2008 financial crisis had scattered incredulity around the globe regarding traditional financial systems, which made investors and non-financial customers turn to other alternative such as digital banking systems. The existence and development of blockchain technology make cryptocurrency in recent years believably become a complete alternative to traditional ones. Bitcoin is the world's first peer-to-peer and decentralized digital cash system initiated by Nakamoto [1]. Though being the most prominent cryptocurrency, Bitcoin has not been a legal trading currency in various countries. Its exchange rate has appeared to be an exceptionally high-risk portfolio with extreme volatility, which requires a more detailed evaluation before making any decision. This paper utilizes knowledge of statistics for financial time series and machine learning to (i) fit the parametric distribution and (ii) model and forecast the volatility of Bitcoin returns, and (iii) analyze its correlation to other financial market indicators. The fitted parametric time series model significantly outperforms other standard models in explaining the stylized facts and statistical variances in the behavior of Bitcoin returns. The model forecast also outperforms some machine learning methodologies, which would benefit policy makers, banks and financial investors in trading activities for both long-term and short-term strategies.
Jeffrey Chu, Stephen Chan, Saralees Nadarajah, Joerg Osterrieder
With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms of five criteria. Conclusions are drawn on the best fitting models, forecasts and acceptability of value at risk estimates.
Pedro Bonillo Bueno, Emilio Aragon Fortes, Konstantinos Vlachoski
Since its launch in 2008, Bitcoin becomes one of the most successful and fast-growing alternative currencies. As of 2017, the market capitalization is around $46 billion and arguably expected to continue growing. The Bitcoin to the US dollar exchange rate has been very volatile and fluctuating significantly. Although Bitcoin was designed as a medium of exchange, it is now more as an investment tool and thus the development of effective quantitative risk management tools becomes quite urgent for all the market participants. In this paper, we investigate empirical distribution of the Bitcoin exchange rate returns by using four types of widelyused heavy-tailed distribution and show that the Skewed t distribution has the best empirical performance. We further calculate the VaR based risk measures and found the Skewed t distribution generates the VaR values, which are closest to historical VaR values. Our results could be directly used in the industry’s stress testing practice, and help financial institutions fulfill the regulatory requirements.
Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP--USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP--USD exchange rate, Bitcoin was robust to Brexit.
The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst\nexponent $H>0.5$, is exploited in order to predict future BTC/USD price. A\nMonte Carlo simulation with $10^4$ geometric fractional Brownian motion\nrealisations is performed as extensions of historical data. The accuracy of\nstatistical inferences is 10\\%. The most probable Bitcoin price at the\nbeginning of 2018 is 6358 USD.\n
We provide an extreme value analysis of the returns of Bitcoin. A particular focus is on the tail risk characteristics and we will provide an in-depth univariate extreme value analysis. Those properties will be compared to the traditional exchange rates of the G10 currencies versus the US dollar. For investors, especially institutional ones, an understanding of the risk characteristics is of utmost importance. So for Bitcoin to become a mainstream investable asset class, studying these properties is necessary. Our findings show that the bitcoin return distribution not only exhibits higher volatility than traditional G10 currencies, but also stronger non-normal characteristics and heavier tails. This has implications for risk management, financial engineering (such as bitcoin derivatives) — both from an investor's as well as from a regulator's point of view. To our knowledge, this is the first detailed study looking at the extreme value behavior of the cryptocurrency Bitcoin.
In the era of diminishing power from US dollar and increasing competition among world currencies, Bitcoin, as a completely new concept as a medium of exchange, has received increasing attentions over the world. Nowadays, Bitcoin also becomes an investment vehicle, which carries attractive opportunities but also significant risks for the investment community. In this paper, we have compared the empirical performance of a newly-developed heavy-tailed distribution, the normal reciprocal inverse Gaussian (NRIG), with the most popular heavy-tailed distribution, the Student’s t distribution, under the GARCH framework in fitting the daily Bitcoin exchange rate returns. Our results indicate the heavy-tailed distribution has better performance in capture the daily Bitcoin exchange rate returns dynamics than the standard normal distribution. Our results also show the older fashioned Student’s t distribution still performs better than the new heavy-tailed distribution.
Digital currencies and cryptocurrencies have hesitantly started to penetrate the investors, and the next step will be the regulatory risk management framework. We examine the Value-at-Risk and Expected Shortfall properties for the major digital currencies, Bitcoin, Ethereum, Litecoin, and Ripple. The methodology used is GARCH modelling followed by Filtered Historical Simulation. We find that digital currencies are subject to a higher risk, therefore, to higher sufficient buffer and risk capital to cover potential losses.
From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences Mentors: Mina Lee and Li Yang
Joerg Osterrieder, Stephen Chan, Jeffrey Chu, Saralees Nadarajah
We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single distribution fits well jointly to all the cryptocurrencies analysed. We find that for the most popular currencies, such as Bitcoin and Litecoin, the generalized hyperbolic distribution gives the best fit, while for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalized t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.