We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals used to capture the non-Gaussian cryptocurrency return dynamics. Based on the time series model, we optimize the portfolio in terms of Foster-Hart risk. Those sophisticated techniques are not yet documented in the context of cryptocurrency. Statistical tests suggest that the MNTS distributed GARCH model fits better with cryptocurrency returns than the competing GARCH-type models. We find that Foster-Hart optimization yields a more profitable portfolio with better risk-return balance than the prevailing approach.
This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better than other models. Moreover, the EGARCH model's asymmetric term is positive and insignificant, which suggests that Bitcoin prices lack the asymmetric volatility response to past returns. Finally, we formulate an option trading strategy by exploiting the volatility spread between the GARCH volatility forecast and the option's implied volatility. We show that a simple volatility-spread trading strategy with delta-hedging can yield robust profits.
Previous studies have shown that cryptocurrencies could hedge equities. However, most of those studies did not take into account the recent cryptocurrencies bubbles in 2018 and domestic currencies. Therefore, this research aimed to study whether the hedge effectiveness of cryptocurrencies still exists. This research used five cryptocurrencies (bitcoin, ethereum, monero, ripple, and litecoin), equity indices (Indonesia, Malaysia, Vietnam, Thailand, and the Philippines), and iShares ETF MSCI World (developed world). Commodities-based hedging using iShares S&P GSCI Commodity-Indexed Trust was also analyzed as a comparison. The asymmetric generalized dynamic conditional correlation (AG-DCC) GARCH showed that one cryptocurrency could not significantly and consistently hedge equities while five equally weighted cryptocurrencies could marginally hedge equities. Meanwhile, the classical minimum variance model also showed that the hedge effectiveness of cryptocurrencies was insignificantly positive. Equity traders could add cryptocurrencies into portfolios when the purpose was to maximize the Sharpe ratio instead of hedging. Overall, commodities were the better hedge for Southeast Asia emerging markets.
While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $Ό$ of the cumulative return distribution exhibits $Ό\approx 3$, which is referred to as "the inverse cubic law." On the other hand, that of the Bitcoin return is claimed to be $Ό\approx 2$, which is known as "the inverse square law." We investigate the scaling properties using recent Bitcoin data and find that the tail index changes to $Ό\approx 3$, which is consistent with the inverse cubic law. This suggests that some properties of the Bitcoin market could vary over time. We also investigate the autocorrelation of absolute returns and find that it is described by a power-law with two scaling exponents. By analyzing the absolute returns standardized by the realized volatility, we verify that the Bitcoin return time series is consistent with normal random variables with time-varying volatility.
Abstract Being more and more popular in the past 10 years, Bitcoin has drawn extensive attention from the press, scholars, and practitioners. The aim of this paper is to investigate which predictor is more predictive for Bitcoin volatility from the aspects of inâsample and outâofâsample in a highâspeed changing world. We utilise the GARCHâMIDAS model to examine the predictive power of five crucial predictors, including VIX, GVZ, Google Trends, GEPU, and GPR. Our findings provide strong evidence that GVZ exhibits strongest predictability for Bitcoin volatility over other competing predictors. Other empirical results based on different outâofâsample forecasting periods, alternative loss functions and combination methods further ensure our major conclusions are robust.
Shaen Corbet, Yang Hou, Yang Hu, Les Oxley · 5 authors
Utilising Chinese-developed data based on long-standing influenza indices, and the more recently-developed coronavirus and face mask indices, we set out to test for the presence of volatility spillovers from Chinese financial markets upon a broad number of traditional financial assets during the outbreak of the COVID-19 pandemic. Such indices are used to specifically measure the performance of Chinese companies who are inherently involved in the R&D and production of materials and products used to mitigate and counteract the effects of influenza and coronavirus, therefore, such indices present a unique barometer of broad population-based sentiment relating to COVID-19 in comparison to traditional Chinese influenza. Within days of the formal announcement of the COVID-19 outbreak, results indicate exceptionally pronounced and persistent impacts of the coronavirus pandemic upon Chinese financial markets, compared to that of the traditional and long-standing influenza index. Further, in a novel finding to date, COVID-19 is found to have had a substantial effect on directional spillovers upon the Bitcoin market. Cryptocurrency-based confidence appears to have been instigated through government-developed education schemes, which are identified as one possible explanation for our results, which are found to remain robust across both data-frequency and methodological variation.
Abstract This paper evaluates the presence of regime changes in the logâreturns volatility dynamics of cryptocurrencies using MarkovâSwitching GARCH (MSâGARCH) models. The empirical study compares the prediction performance of MSâGARCH against traditional singleâregime GARCH methods for oneâ, fiveâ and tenâstepsâahead volatility forecasting of six leading digital coins such as Bitcoin, Dashcoin, Ethereum, Litecoin, Monero and Ripple. Using a Bayesian approach, different MSâGARCH structures are estimated considering specifications up to three regimes, three scedastic functions and six error distributions, resulting in a total of 54 models for each cryptocurrency. Forecasts are compared according to an economic criterion, that is, through the estimation of ValueâatâRisk (VaR) and Expected Shortfall (ES) risk measures. The results support the evidence of regime changes in the volatility process of selected cryptocurrencies and show that MSâGARCH models do provide more accurate VaR and ES forecasts than their singleâregime counterparts.
Abstract This study investigates whether Bitcoin (BTC) can provide a hedge against the fiat currencies in Asia over various investment horizons. We focus on Asia because it is one of the fastestâgrowing regions worldwide, where cryptocurrencies are actively traded. A wavelet transform technique is combined with a multivariate factor stochastic volatility (SV) model to examine the dynamic correlation properties and risk reduction effectiveness of BTC in both the time and frequency domains. We use gold and oil as benchmarks and compared their results with those of BTC. The estimated correlations indicate that the Asian currencies tend to be negatively correlated with BTC; therefore, the latter could provide a hedge against the former over the medium (8â32 days) and long (32â64 days) terms. By contrast, Asian currencies tend to be positively correlated with oil and gold for the same horizons. We also analyze the downside risk reduction effectiveness of BTC for the portfolio of Asian currencies and find that BTC provides better risk reduction than oil and gold, particularly over the medium and long terms. This study makes significant contributions to the literature by demonstrating that the correlation properties and risk reduction effectiveness of BTC differ depending on the investment horizons. We believe our findings using the waveletâbased SV model can help heterogeneous investors detect portfolio risks and thus, identify optimal hedging strategies over various investment horizons.
OlaOluwa S. Yaya, Xuan Vinh Vo, Ahamuefula E. Ogbonna, Adeolu O. Adewuyi
Abstract This paper empirically provides support for fractional cointegration of high and low cryptocurrency price series, using particularly, Bitcoin, Ethereum, Litecoin and Ripple; synchronized at different high time frequencies. The difference of high and low price gives the price range, and the rangeâbased estimator of volatility is more efficient than the returnâbased estimator of realized volatility. A more general fractional cointegration technique applied is the Fractional Cointegrating Vector Autoregressive framework. The results show that high and low cryptocurrency prices are actually cointegrated in both stationary and nonâstationary levels; that is, the range of highâlow price. It is therefore quite interesting to note that the fractional cointegration approach presents a lower measure of the persistence for the range compared to the fractional integration approach, and the results are insensitive to different time frequencies. The main finding in this work serves as an alternative volatility estimation method in cryptocurrency and other assets' price modelling and forecasting.
The main purpose of our paper is to evaluate the impact of the COVID-19 pandemic on randomness in volatility series of world major markets and to examine its effect on their interconnections. The data set includes equity (Bitcoin and Standard and Poorâs 500), precious metals (Gold and Silver), and energy markets (West Texas Instruments, Brent, and Gas). The generalized autoregressive conditional heteroskedasticity model is applied to the return series. The wavelet packet Shannon entropy is calculated from the estimated volatility series to assess randomness. Hierarchical clustering is employed to examine interconnections between volatilities. We found that (i) randomness in volatility of the S&P500 and in the volatility of precious metals were the most affected by the COVID-19 pandemic, while (ii) randomness in energy markets was less affected by the pandemic than equity and precious metal markets. Additionally, (iii) we showed an apparent emergence of three volatility clusters: precious metals (Gold and Silver), energy (Brent and Gas), and Bitcoin and WTI, and (iv) the S&P500 volatility represents a unique cluster, while (v) the S&P500 market volatility was not connected to the volatility of Bitcoin, energy, and precious metal markets before the pandemic. Moreover, (vi) the S&P500 market volatility became connected to volatility in energy markets and volatility in Bitcoin during the pandemic, and (vii) the volatility in precious metals is less connected to volatility in energy markets and to volatility in Bitcoin market during the pandemic. It is concluded that (i) investors may diversify their portfolios across single constituents of clusters, (ii) investing in energy markets during the pandemic period is appealing because of lower randomness in their respective volatilities, and that (iii) constructing a diversified portfolio would not be challenging as clustering structures are fairly stable across periods.
Chun Kwong Koo, Artur Semeyutin, Chi Keung Marco Lau, Jian Fu
We study the tailsâ behavior of four major Cryptocurrencies (Bitcoin, Litecoin, Ethereum and Ripple) by employing the Autoregressive FrÂŽechet model for conditional maxima. Using five-minute-high-frequency data, we report time-evolving tails as well as provide a straightforward measure of tails asymmetry for positive and negative intra-day returns. We find that only Bitcoin has a notable more massive tail for positive returns asymmetry while the remaining three Cryptocurrencies have a general tendency towards more massive negative intra-day tails. All considered Cryptocurrencies depict lighter tails as the market matures.
Venelina Nikolova, Juan Evangelista Trinidad Segovia, M. FernĂĄndezâMartĂnez, M.A. SĂĄnchez-Granero
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs.
Huthaifa Alqaralleh, Alaâa Adden Abuhommous, Ahmad Alsaraireh
This study is set out to model and forecast the cryptocurrency market by concentrating on several stylized features of cryptocurrencies. The results of this study assert the presence of an inherently nonlinear mean-reverting process, leading to the presence of asymmetry in the considered return series. Consequently, nonlinear GARCH-type models taking into account distributions of innovations that capture skewness, kurtosis and heavy tails constitute excellent tools for modelling returns in cryptocurrencies. Finally, it is found that, given the high volatility dynamics present in all cryptocurrencies, correct forecasting could help investors to assess the unique risk-return characteristics of a cryptocurrency, thus helping them to allocate their capital.
Abstract Cryptocurrencies are unique and extra-ordinary currencies which to be econometrically forced into the linear model due to their systematic complexity and extreme movements. This paper was conducted to provide an alternative analysis as a solution for escaping the restrictions of traditional linear assumptions. Five predominant digital currencies such as Bitcoin (BTC), Stellar network (XLM), Litecoin (LTC), Ethereum Classic (ETC), and IOTA were chosen to be employed in the multiple processes based on Bayesian approaches. Market dominance and data regime classifications are the essential components that lead to successfully investigate the dependent structures and co-movements in the digital financial market. The empirical findings could assume that the modern time-series data was meticulously estimated by the flexible modern tool. Bayesian statistics and simulations have the sufficient potency as the suitable solution.
Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.
The analysis of cryptocurrencies market behaviour is receiving significant attention from researchers and practitioners in the last decades. This paper aims at contributes to volatility estimations of the cryptocurrencies helping to highlight the main stylized facts and characteristics. The performance of different specifications of volatility modelling, within the GARCH class, have been compared through the Model Confidence Set (MCS) over four of the most capitalised cryptocurrencies, namely Bitcoin, Ethereum, Stellar and Ripple. Our empirical findings give evidence of strong asymmetric effects in cryptocurrencies volatility leading to a better performance of asymmetric GARCH specifications..
In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.