A reputation of high volatility accompanies the emergence of Bitcoin as a financial asset. This paper intends to nuance this reputation and clarify our understanding of Bitcoin's volatility. Using daily, weekly, and monthly closing prices and log-returns data going from September 2014 to January 2021, we find that Bitcoin is a prime example of an asset for which the two conceptions of volatility diverge. We show that, historically, Bitcoin allies both high volatility (high Standard Deviation) and high predictability (low Approximate Entropy), relative to Gold and S&P 500. Moreover, using tools from Extreme Value Theory, we analyze the convergence of moments, and the mean excess functions of both the closing prices and the log-returns of the three assets. We find that the closing price of Bitcoin is consistent with a generalized Pareto distribution, when the closing prices of the two other assets (Gold and S&P 500) present thin-tailed distributions. However, returns for all three assets are heavy tailed and second moments (variance, standard deviation) non-convergent. In the case of Bitcoin, lower sampling frequencies (monthly vs weekly, weekly vs daily) drastically reduce the Kurtosis of log-returns and increase the convergence of empirical moments to their true value. The opposite effect is observed for Gold and S&P 500. These properties suggest that Bitcoin's volatility is essentially an intra-day and intra-week phenomenon that is strongly attenuated on a weekly time-scale, and make it an attractive store of value to investors and speculators, but its high standard deviation excludes its use a currency.
Beata Szetela, Grzegorz Mentel, Yuriy Bilan, Urszula Mentel
Abstract The aim of the paper is to verify the existence of short- and long-term relationships between the strength of a trend and the volume in bullish and bearish cryptocurrency markets. We applied the vector error correction model to bitcoin daily data from 14.01.2015 to 22.12.2019. Based on the prices and following Wilderâs algorithm, the average directional movement index was calculated, and upward and downward trend periods were determined. No long-term relationship was found to exist between the strength of a trend and the volume in both bearish and bullish markets. Hence, trends do not react to volume changes. However, a long-term relationship exists between volume and trendâbut only for the downward trendâwith an adjustment speed of 88%. In the short-term, a statistically significant but very weak dependency is revealed; hence, the conclusion that trend strength is insensitive to volume changes can be reached.
Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the priceâvolatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes. The conventional GARCH-class models have shown that in cryptocurrency markets, asymmetric reactions of volatility to returns differ from those of other traditional financial assets. We address this issue from a viewpoint of fractal analysis, which can cover the nonlinear interactions and the self-similarity properties widely acknowledged in the field of econophysics. The asymmetric cross-correlations between price and volatility for Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), and Litecoin (LTC) during the period from June 1, 2016 to December 28, 2020 are investigated using the MF-ADCCA method and quantified via the asymmetric DCCA coefficient. The approaches take into account the nonlinearity and asymmetric multifractal scaling properties, providing new insights in investigating the relationships in a dynamical way. We find that cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH. In contrast, for XRP and LTC, inverted reactions are present where cross-correlations are stronger in uptrend markets.
This paper empirically examines jumps and cojumps of both major and minor cryptocurrencies. Understanding the nature of their jumps and cojumps plays an important role in risk management, asset allocation and pricing of derivatives. We find that all cryptocurrencies display significant jumps. Furthermore, minor cryptocurrencies appear to have significantly higher jump intensity and jump size than major cryptocurrencies. Finally, we find that cojumps of the Thai stock market index and minor cryptocurrencies have a greater intensity than that of major cryptocurrencies.
This paper studies the dynamics of cryptocurrency volatility using a stochastic volatility model with simultaneous and correlated jumps in returns and volatility. We estimate the model using an efficient sequential learning algorithm that allows for learning about multiple unknown model parameters simultaneously, with daily data on four popular cryptocurrencies. We find that these cryptocurrencies have quite different volatility dynamics. In particular, they exhibit different return-volatility relationships: While Ethereum and Litecoin show a negative relationship, Chainlink displays a positive one and interestingly, Bitcoinâs one changes from negative to positive in June 2016. We also provide evidence that the sequential learning algorithm helps better detect large jumps in the cryptocurrency market in real time. Overall, incorporating volatility jumps helps better capture the dynamic behavior of highly volatile cryptocurrencies.
This study investigates the volatility of daily Bitcoin returns and multifractal properties of the Bitcoin market by employing the rolling window method and examines relationships between the volatility asymmetry and market efficiency. Whilst we find an inverted asymmetry in the volatility of Bitcoin, its magnitude changes over time, and recently, it has become small. This asymmetric pattern of volatility also exists in higher frequency returns. Other measurements, such as kurtosis, skewness, average, serial correlation, and multifractal degree, also change over time. Thus, we argue that properties of the Bitcoin market are mostly time dependent. We examine efficiency-related measures: the Hurst exponent, multifractal degree, and kurtosis. We find that when these measures represent that the market is more efficient, the volatility asymmetry weakens. For the recent Bitcoin market, both efficiency-related measures and the volatility asymmetry prove that the market becomes more efficient.
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 models better depicted asymmetries in cryptocurrencies' volatility and revealed persistence and "intensifying" levels in their volatility. The IGARCH was the best performing model for Monero. As for the remaining cryptocurrencies, the GJR-GARCH model proved to be superior during the in-sample period while the CGARCH and TGARCH specifications were the optimal ones in the out-of-sample interval. The VaR forecasting performance is enhanced with the use of the asymmetric GARCH models. The VaR results provided a very accurate measure in determining the level of downside risk exposing the selected exchange currencies at all confidence levels. However, the outcomes were far from being uniform for the selected cryptocurrencies: convincing for Dash and Dogcoin, acceptable for Litecoin and Monero and unconvincing for Bitcoin and Ripple, where the (optimal) model was not rejected only at the 99% confidence level.
The development process in financial markets give rise to the emergence of various financial instruments and cryptocurrencies, which are the newest tools of this process, are trying to integrate into the system. Even though the use of crypto-currencies for investment and speculation has increased, limited information on the market leads to high level of volatility in price and return. Therefore, this study aims to analyze the volatility dynamics of the returns of Bitcoin, which is the cryptocurrency with the largest market volume, using the weekly data set for 2013:04-2020:09 period. In this context, Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model is employed to investigate the asymmetric volatility, which refers to the asymmetric effects of positive and negative shocks. The results of the analysis show that the leverage effect applies to Bitcoin returns. In other words, the asymmetric effect between good and bad news is revealed. Moreover, the fact that the parameter of the volatility resistance has a high value reflects that the asymmetric past period shocks have a significant effect on the current period conditional variance.
We consider the hedging problem where a futures position can be automatically\nliquidated by the exchange without notice. We derive a semi-closed form for an\noptimal hedging strategy with dual objectives - to minimise both the variance\nof the hedged portfolio and the probability of liquidations due to insufficient\ncollateral. The optimal solution depends on the statistical characteristics of\nthe spot and futures extreme returns and parameters that characterise the\nhedger by loss aversion, choice of leverage and collateral management. An\nempirical analysis of bitcoin shows that the optimal strategy combines superior\nhedge effectiveness with a reduction in the probability of liquidation. We\ncompare the performance of seven major direct and inverse hedging instruments\ntraded on five different exchanges, based on minute-level data. We also link\nthis performance to novel speculative trading metrics, which differ markedly\nbetween venues.\n
COVID-19 pandemic has caused significant losses and an increase in the level of risk in the financial markets and global economy. Thus in this study, we model the crypto market volatility behavior during the COVID-19 crisis. GARCH (1, 1) and GJR-GARCH (1, 1) were applied to model the volatility clustering and leverage effects in the intraday day (15-minute interval) returns of Bitcoin, Ethereum, and Litcoin ranging from 11th April 2019 to 8th February 2021. The empirical findings from GARCH (1, 1) model indicates the presence of volatility clustering in the crypto market. Moreover, the results of the GJR-GARCH (1, 1) indicate the presence of leverage effects in the financial returns series of all three crypto currencies. Furthermore, the excess kurtosis confirms the existence of fat-tail phenomena in the crypto market. Overall, the findings from this study showed that in times of COVID 19 pandemic the crypto market returns series showed volatility persistence, fat-tail phenomena, and leverage effects. These outcomes provide a better understanding for financial investors to invest rationally and cautiously during pandemic times.
In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We found that the option price is indeed lower for our proposed window average lookback option than for a traditional lookback option. We found the Hurst parameter to be H = 0.09 which confirms that the cryptocurrencies market is indeed rough.
This work is a comparative study of different univariate and multivariate time series predictive models as applied to Bitcoin, other cryptocurrencies, and other related financial time series data. ARIMA models, long regarded as the gold standard of univariate financial time series prediction due to both its flexibility and simplicity, are used a baseline for prediction. Given the highly correlative nature amongst different cryptocurrencies, this work aims to show the benefit of forecasting with multivariate time series modelsâprimarily focusing on a novel parameter optimization of VARIMA models outlined in this paper. These models are trained on 3 years of historical data, aggregated from different cryptocurrency exchanges by Coinmarketcap.com, which includes: daily average prices and trading volume. Historical time series data of traditional market data, including the stock Nvidia, the de facto leading manufacture of gaming GPUâs, is also analyzed in conjunction with cryptocurrency prices, as gaming GPUâs have played a significant role in solving the profitable SHA256 hashing problems associated with cryptocurrency mining and have seen equivalently correlated investor attention as a result. Models are trained on this historical data using moving window subsets, with window lengths of 100, 200, and 300 days and forecasting 1 day into the future. Validation of this prediction against the actually price from that day are done with following metrics: Directional Forecasting (DF), Mean Absolute Error (MAE), and Mean Squared Error (MSE).
We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives - to minimise both the variance of the hedged portfolio and the probability of liquidations due to insufficient collateral. The optimal solution depends on the statistical characteristics of the spot and futures extreme returns and parameters that characterise the hedger by loss aversion, choice of leverage and collateral management. An empirical analysis of bitcoin shows that the optimal strategy combines superior hedge effectiveness with a reduction in the probability of liquidation. We compare the performance of seven major direct and inverse hedging instruments traded on five different exchanges, based on minute-level data. We also link this performance to novel speculative trading metrics, which differ markedly between venues.
The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ modelâs calibration over others for pricing Bitcoin options.
Since the advent of Bitcoin, the cryptocurrency market has become an important financial market. However, due to the existence of the cryptocurrency bubble, investors face more difficulties in risk portfolios. We adopt wavelet packet decomposition, nonlinear Granger causality test, risk spillover network, and STVAR model; retain the mature research of multiscale systemic risk based on time and frequency; and thus extend systemic risk to different regimes. We found that when frequency is combined with regimes, the risk spillover center will undergo subversive changes in the long run. We also proposed that BTC will be more robust at extreme values (like longest and shortest periods), while cryptocurrencies with smaller market capitalization will be stronger in the medium term. At the same time, the recession period will also spur on it.
The cryptocurrency market recently gained a lot of attention from investors. But, its volatility has been acting as a disincentive to investment. Volatility plays an important role in shaping market riskiness and investment behavior. We study the volatility of the Ethereum (ETH) cryptocurrency from the following perspectives. The first goal of this study is to identify risk-seeking behavior in the ETH cryptocurrency market. We examine this propensity by measuring the effect of the volatility of Ethereum on the total ETH assets. This investigation also takes the form of a case-study of an unexpected ETH fund-stolen event, DAO Hack, and the hard fork treatment. We also forecast a downward volatility trend in the near future based on Autoregressive models. This is the first study to analyze DAO Hack with empirical methods and marks the starting point for more rigorous models to predict the volatility of Ethereum.
This paper implements the analysis of volatility behaviour of the eight major cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, Monero, Stellar, Dash and Tether) for the period starting from October 13th 2015 to November 18th 2019. The GARCH-type models with heavy-tailed distributions are fitted to filter the conditional volatility exhibited by cryptocurrencies. Extreme value analysis based on the peak over threshold approach is then used to model the extreme tail behaviour of the cryptocurrencies. The predictive performance of the GARCH-EVT model in forecasting Value-at-Risk is evaluated at both 5% and 1% levels of significance. The backtesting results demonstrate the superiority of the GARCH-EVT model in both out-of-sample forecasts and goodness-of-fit properties to cryptocurrency returns and forecasting Value-at-Risk. Overall, the empirical results of this study recommend the heavy-tailed GARCH-EVT based model for modelling and forecasting the volatility of cryptocurrencies.
We investigate the dynamics of daily realised returns and risk premiums for a large cross-section of cryptocurrency pairs through the lens of an Instrumented Principal Component Analysis (IPCA) (see Kelly et al., 2019). We show that a model with three latent factors and time-varying factor loadings significantly outperforms a benchmark model with observable risk factors: the total (predictive) R2 from the IPCA is 17.2% (2.9%) for individual returns, against a benchmark 9.6% (-0.02%) obtained from a model with six observable risk factors explored in previous literature. By looking at the characteristics that significantly matter for the dynamics of risk premiums, we provide robust evidence that liquidity, size, reversal, and both market and downside risks represent the main driving factors behind expected returns. These results hold for both individual assets and characteristic-based portfolios, pre and post the Covid-19 outbreak, and for weekly individual and portfolio returns.
This study investigates how uncertainty surrounding cryptocurrency affects cryptocurrency return (CR) by employing various wavelet techniques. To this end, we concentrate on the recently published cryptocurrency uncertainty index (UCRY) and the top eight cryptocurrencies by virtue of market capitalization for the period from December 30, 2013, until February 21, 2021. Our results show that the UCRY index strongly predicts CR. In particular, the UCRY index has a leading position in all the frequencies for all cryptocurrencies in our sample. Additionally, when the impacts of economic policy uncertainty and the volatility index are eliminated, the significant co-movement of UCRY-CR stays unchanged for short-, medium-, and long-term investment horizons. Thus, we conclude that the UCRY-CR relationships are both persistent and pervasive. Our study contributes to the literature on the relationships between cryptocurrency and market uncertainties as well as to investors who use uncertainty indices to design their investment strategies for their portfolios.
Francis Liu, Natalie Packham, Meng-Jou Lu, Wolfgang Karl HĂ€rdle
The introduction of derivatives on Bitcoin enables investors to hedge risk exposures in cryptocurrencies. Because of volatility swings and jumps in cryptocurrency prices, the traditional variance-based approach to obtain hedge ratios may not be suitable for hedgers. In this work, we consider two extensions of the traditional approach: first, different dependence structures are modelled by different copulae, such as the Gaussian, Student-t, Normal Inverse Gaussian and Archimedean copulae; second, different risk measures, such as value-at-risk, expected shortfall and spectral risk measures are employed to find the optimal hedge ratio. Extensive out-of-sample tests using the data from the time period December 2017 until May 2021 give insights in the practice of hedging various cryptos and crypto indices, including Bitcoin, Ethereum, Cardano, the CRIX index and a number of crypto-portfolios. Evidence shows that BTC futures can effectively hedge BTC and BTC-involved indices. This promising result is consistent across different risk measures and copulae except for the Frank copula. On the other hand, we observe complex and diverse dependence structures between non-BTC-related cryptocurrencies and the BTC futures. As a consequence, the hedge performance of non-BTC-related cryptocurrencies is mixed and even suitable for some assets.