This paper compares a number of stochastic volatility (SV) models for modeling and predicting the volatility of the four most capitalized cryptocurrencies (Bitcoin, Ethereum, Ripple, and Litecoin). The standard SV model, models with heavy-tails and moving average innovations, models with jumps, leverage effects and volatility in mean were considered. The Bayes factor for model fit was largely in favor of the heavy-tailed SV model. The forecasting performance of this model was also found superior than the other competing models. Overall, the findings of this study suggest using the heavy-tailed stochastic volatility model for modeling and forecasting the volatility of cryptocurrencies.
This paper studies of the multifractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that cryptocurrencies have different degree of long range dependence, and --more importantly -- follow different stochastic processes. Some of them follow models closer to monofractal fractional Gaussian noises, while others exhibit complex multifractal dynamics. Regarding the source of multifractality, our results are mixed. Time series shuffling produces a reduction in the level of multifractality, but not enough to offset it. We find an association of kurtosis with multifractality.
This letter expands the studies of the informational efficiency in the cryptocurrency market. Most studies have focused on Bitcoin, the foremost known cryptocurrency, and a few more coins. However, this market is more diverse, with cryptocurrencies entering and leaving the market on a weekly basis. This letter fills an important gap in the literature, by studying the informational efficiency using a multi-scaling methodology, which represents a new approach. We compute the generalized Hurst exponent of eighty-four cryptoassets daily returns. The multi-scaling methodology used in this paper find compelling evidence that cryptocurrencies have different degree of long range dependence, and --more importantly -- follow different stochastic processes. Some of them follow traditional monofractal models consistent with fractional Brownian motion, while others exhibit complex multifractal dynamics.
In recent years cryptocurrency trading has captured the attention of practitioners and academics. The volume of the exchange with standard currencies has known a dramatic increasing of late. This paper addresses to the need of models describing a bitcoin-US dollar exchange dynamic and their use to evaluate European option having bitcoin as underlying asset.
Abstract This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.
Saiful Izzuan Hussain, Nadiah Ruza, Nurulkamal Masseran, Muhammad Aslam Mohd Safari
Dependence structure between financial assets plays an important role in risk management. This research investigates the dependence pattern between the stock market and the potential of cryptocurrency. We employed time- varying copula and Extreme Value Theory (EVT) to model the extreme dependence between the United States (US) index stock market (S&P500) and Bitcoin. Empirical results show risk diversification for holdings of the S&P500 and Bitcoin during extreme events seem to be effective. This paper contributes to a better understanding of the dependence structure of the financial market during extreme events. This information is useful for investors who are seeking for the cross-market diversification.
Finansal zaman serilerinde görülen değişen varyans sorununun (ARCH etkisi) sonucu olarak otoregresif koşullu değişen varyans modelleri bulunmuştur. Çalışmamızda, piyasa değeri en yüksek üç kripto paranın [Bitcoin (BTC), Ethereum (ETH) ve Ripple (XRP)] getirileri incelenmiş ve söz konusu getirilerde finansal zaman serilerine benzer şekilde ARCH etkisi bulunmuştur. Söz konusu üç kripto paranın volatiliteleri için en iyi modelin hesaplanmasında altı GARCH modelini karşılaştırılmıştır. Bu modeller sırasıyla GARCH (1,1), EGARCH (1,1), TGARCH (1,1), APARCH (1,1), CGARCH (1,1) ve ACGARCH (1,1) modellerinden oluşmaktadır. Çalışma kapsamında 01.10.2015 - 01.10.2018 tarihleri arasında Bitcoin (BTC), Ethereum (ETH) ve Ripple (XRP) kripto paralarının günlük kapanış verilerinden elde edilen getiriler kullanılmıştır. Volatilite tahminlerinde Bitcoin (BTC) ve Ethereum (ETH) için en iyi model EGARCH (1,1), Ripple (XRP) için ise APARCH (1,1) modeli bulunmuştur. Çalışma kapsamında bu modeller kullanılarak volatiliteler üzerinde negatif şokların pozitif şoklardan daha fazla etkisinin bulunduğunu gösteren kaldıraç etkisi incelenmiştir. Bitcoin (BTC) ve Ethereum (ETH) modellerinde kaldıraç etkisi bulunmamış, bununla birlikte pozitif şoklar negatif şoklara göre daha fazla volatiliteye neden olmuştur. Ancak, Ripple (XRP) volatilite modelinde kaldıraç etkisi belirlenmiştir.
Since it was invented by Satoshi Nakamoto in 2008, Bitcoin has drawn considerable attention both from the financial industry and government supervisory departments, and there is no unanimity on Bitcoin’s nature in the academic field. Some people may think Bitcoin is more like an asset than a currency. And investors’ motivations for incorporating Bitcoin into their portfolios may vary. Might there be a better way to deal with the risk-detection issue associated with such a unique and ambiguous object? The copula-GARCH method has been proven in much of the literature to be a better way than the traditional ways to estimate the value at risk (VaR) of portfolios. When it comes to a portfolio containing Bitcoin, can it still maintain its superiority? In this study, gold and Ethereum were each used to construct a portfolio with Bitcoin. We collected a total of 2,246 daily adjusted closing prices from July 23, 2010, to March 12, 2019. As for the copula-GARCH model, we selected four constant and two time-varying copula models combined with GARCH Student-t residuals to fit the joint distribution of the two assets in the portfolios. The traditional methods refer to the historical simulation, the variance-covariance method, the EWMA method, and the univariate GARCH VaR method. We adopted each method to compute corresponding one-day VaRs. Our results indicated that for the portfolios containing Bitcoin and Ethereum, the copula-GARCH method performed better than traditional methods, while for the portfolio consisting of Bitcoin and gold, traditional methods performed better. Our results may suggest that the copula-GARCH method may not be suitable in the extremely low correlation case.
In this paper, two univariate generalised autoregressive conditional heteroskedasticity (GARCH) option pricing models are applied to Bitcoin and the Cryptocurrency Index (CRIX). The first model is symmetric and the other takes asymmetric effects into account. Furthermore, the accuracy of the GARCH option pricing model applied to Bitcoin is tested. Empirical results indicate that asymmetry is not an important factor to consider when pricing options on Bitcoin or CRIX, this is consistent with findings in the literature. In addition, the GARCH option pricing model provides realistic price discovery within the bid-ask spreads suggested by the market.
Muhammad Abubakr Naeem, Kashif Saleem, Sheraz Ahmed, Naeem Muhammad · 5 authors
We explore extreme return-volumes dependence among different cryptocurrencies such as Bitcoin, Ethereum, Ripple, and Litecoin by using the Copula approach. We use Student-t, Frank, Clayton, Survival Clayton, Gumbel, and SJC copulas. We filter out margins by using the EGARCH model for return series and GARCH model for volume series. Evidence of significant symmetric dependence between return-volume is not found due to insignificance of student-t and Frank copula parameters. In a return-volume relationship, coefficients of lower tail dependence are significant for Bitcoin, Ripple, and Litecoin which means that low returns are followed by low volumes. Lower tail dependence for the return-volume relationship is stronger than the upper tail dependence for Bitcoin, Ripple, and Litecoin. Moreover, for negative return-volume, left tail dependence coefficients are significant for Ripple and Litecoin, which means that high returns are followed by low volumes for Ripple and Litecoin. Our investigation shows that investors (buyer or seller) are very careful in extreme market conditions for both Ripple and Litecoin. Extreme upper tail and lower tail dependence coefficients are insignificant for Ethereum.
Purpose Cryptocurrency markets are notoriously noisy, but not all markets might behave in the exact same way. Therefore, the aim of this paper is to investigate which one of the cryptocurrency markets contributes the most to the common volatility component inherent in the market. Design/methodology/approach The paper extracts each of the cryptocurrency's markets' latent volatility using a stochastic volatility model and, subsequently, models their dynamics in a fractionally cointegrated vector autoregressive model. The authors use the refinement of Lien and Shrestha (2009, J. Futures Mark) to come up with unique Hasbrouck (1995, J. Finance) information shares. Findings The authors’ findings indicate that Bitfinex is the leading market for Bitcoin and Ripple, while Bitstamp dominates for Ethereum and Litecoin. Based on the dominant market for each cryptocurrency, the authors find that the volatility of Bitcoin explains most of the volatility among the different cryptocurrencies. Research limitations/implications The authors’ findings are limited by the availability of the cryptocurrency data. Apart from Bitcoin, the data series for the other cryptocurrencies are not long enough to ensure the precision of the authors’ estimates. Originality/value To date, only price discovery in cryptocurrencies has been studied and identified. This paper extends the current literature into the realm of volatility discovery. In addition, the authors propose a discrete version for the evolution of a markets fundamental volatility, extending the work of Dias et al. (2018).
Abstract This paper studies a large number of bitcoin (BTC) options traded on the options exchange Deribit. We use the trades to calculate implied volatility (IV) and analyze if volatility forecasts can be improved using such information. IV is less accurate than AutoRegressive–Moving‐Average or Heterogeneous Auto‐Regressive model forecasts in predicting short‐term BTC volatility (1 day ahead), but superior in predicting long‐term volatility (7, 10, 15 days ahead). Furthermore, a combination of IV and model‐based forecasts provides the highest accuracy for all forecasting horizons revealing that the BTC options market contains unique information.
María Belén Arouxét, Aurelio F. Bariviera, Verónica Pastor, Victoria Vampa
Cryptocurrency history begins in 2008 as a means of payment proposal. However, cryptocurrencies evolved into a complex ecosystem of high yield speculative assets. Contrary to traditional financial instruments, they are not (mostly) traded in organized, law-abiding venues, but on online platforms, where anonymity reigns. This paper examines the long term memory in return and volatility, using high frequency time series of seven important coins. Our study covers the pre-Covid-19 and the subsequent pandemic period. We use a recently developed method, based on the wavelet transform, which provides more robust estimators of the Hurst exponent. We detect that, during the peak of Covid-19 pandemic (around March 2020), the long memory of returns was only mildly affected. However, volatility suffered a temporary impact in its long range correlation structure. Our results could be of interest for both academics and practitioners.
Abstract By computing a volatility index (CVX) from cryptocurrency option prices, we analyze this market’s expectation of future volatility. Our method addresses the challenging liquidity environment of this young asset class and allows us to extract stable market implied volatilities. Two alternative methods are considered to compute volatilities from granular intra-day cryptocurrency options data, which spans over the COVID-19 pandemic period. CVX data therefore capture ‘normal’ market dynamics as well as distress and recovery periods. The methods yield two cointegrated index series, where the corresponding error correction model can be used as an indicator for market implied tail-risk. Comparing our CVX to existing volatility benchmarks for traditional asset classes, such as VIX (equity) or GVX (gold), confirms that cryptocurrency volatility dynamics are often disconnected from traditional markets, yet, share common shocks.
Guglielmo Maria Caporale, Woo-Young Kang, Fabio Spagnolo, Nicola Spagnolo
This paper examines mean and volatility spillovers between three major cryptocurrencies (Bitcoin, Litecoin and Ethereum) and the role played by cyber-attacks. Specifically, trivariate GARCH-BEKK models are estimated which include suitably defined dummies corresponding to different types, targets and number per day of cyber-attacks. Significant dynamic linkages (interdependence) between the three cryptocurrencies under investigation are found in most cases when cyber-attacks are taken into account, Bitcoin appearing to be the dominant cryptocurrency. Further, Wald tests for parameter shifts during episodes of turbulence resulting from cyber-attacks provide evidence that the latter affect the transmission mechanism between cryptocurrency returns and volatilities (contagion). More precisely, cyber-attacks appear to strengthen cross-market linkages, thereby reducing portfolio diversification opportunities for cryptocurrency investors. Finally, the conditional correlation analysis confirms the previous findings.
We use a GARCH dummy model to study the influence of calendar effects on daily conditional returns and volatility of Bitcoin during the period 2013–2019. The Halloween, day-of-the-week (DOW), and month-of-the-year (MOY) effects are analyzed. Our results reveal no evidence of a Halloween calendar anomaly. A classical DOW effect is not present in Bitcoin returns, however, we find significantly lower risk over the weekend whilst in the beginning of the week Bitcoin's volatility is more intense. Moreover, supporting evidence of a reverse January effect is detected. Our results also show that investors’ risk drops substantially in September.
This paper aims to examine the relationship between Bitcoin and preeminent financial indicators using Copula-GARCH method. In the study, we use closing prices of Bitcoin and US 10-Year Bond Yield, Gold Spot US Dollar, US Dollar Index, S&P 500, FTSE 100 and NIKKEI 225. To our knowledge, our paper is the first to examine this issue empirically. Analysis results show that there is no strong interdependence between Bitcoin and preeminent financial indicators. These findings provide new information that will benefit policy makers, banks, financial investors, and risk managers in trading activities for both long-term and short-term strategies.