In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the cryptocurrency market into a single framework. We reach the following conclusions in both markets: first, price diffusion and jump ambiguity mainly determine detection-error probability; second, optimal choice is more significantly affected by price diffusion ambiguity than by jump ambiguity, and trivially affected by volatility diffusion ambiguity. In addition, investors tend to be more aggressive in a stable market than in a volatile one. Next, given a larger volatility jump size, investors tend to increase their portfolio during downward price jumps and decrease it during upward price jumps. Finally, the welfare loss caused by price diffusion ambiguity is more pronounced than that caused by jump ambiguity in an incomplete market. These findings enrich the extant literature on effects of ambiguity on the traditional stock market and the evolving cryptocurrency market. The results have implications for both investors and regulators.
The price of cryptocurrency is always volatile and is influenced by various factors like market returns, prices of stocks, gold, and correlation of prices of cryptocurrency. Modeling and forecasting the prices of cryptocurrencies and measuring the volatility with the GARCH specification (Engle, 1982) has become standard among researchers. Several applications and extensions of GARCH model is proposed by Bollerslev (1986). Later, an integrated GARCH model (Engle & Bollerslev, 1986) states that the persistence parameter is equal to one. A combination of short and long memory conditional models for the mean and the volatility to analyze crypto returns is done with the help of ARFIMA (Autoregressive Fractionally Integrated Moving Average) and FIGARCH (Fractionally Integrated Generalized Autoregressive Conditionally Heteroskedastic) Model. This paper intended to understand various mathematical models for volatility of crypto currencies and also to find research gaps in the existing literature. A comprehensive overview is the need of the study.
Roberto Mota Navarro, F. Leyvraz, HernĂĄn Larralde
The study of order volumes in financial markets has shown that these display several non-trivial statistical properties. Most studies have been focused on the bulk properties of volume of incoming orders or of realized transactions rather than the dynamical aspects. The present work is a study of the dynamical properties of volume. Unlike previous works, we studied the volume available at the spread rather than the volume of incoming orders or of realized transactions. We found evidence that suggests mean reverting volume changes and strong asymmetries in the equilibrium of sell and buy orders as well as the presence of clustering.
The current study aims to explore the dynamic connectedness between stock and cryptocurrency markets and to determine the role of cryptocurrencies in the stock market as a hedge, diversifier, or safe haven. The study uses daily data of four stock indices and six cryptocurrencies, covering a period of January 2016 to December 2022. The analysis is conducted using the ADCC-GARC method with the wavelet coherency. The results indicate both stock and cryptocurrency markets exhibit long-run volatility persistence. The properties of Bitcoin, Ethereum, Binance Coin, Dogecoin, and Ripple vary between a range of hedges and diversifiers in different stock markets, which can change depending on market circumstances. However, only Tether has shown that it can act as a safe haven investment in all studied stock markets over time.
Mohammad Ashraful Ferdous Chowdhury, Mohammad Abdullah, Masud Alam, Mohammad Zoynul Abedin · 5 authors
This paper examines the efficiency and asymmetric multifractal features of NFTs, DeFi, cryptocurrencies, and traditional assets using Asymmetric Multifractal Cross-Correlations Analysis covering the period from November 2017 to February 2022. Considering the full sample with a significant variation among asset classes, the study reveals DeFi-DigiByte is the most efficient while the cryptocurrency-Tether is the least efficient. However, S&P 500 showed high efficiency before COVID-19, and DeFi-Enjin Coin advanced as the most efficient asset during COVID-19. The volatility dynamics of NFTs, DeFi, and cryptocurrencies follow strong nonlinear cross-correlations, but evidence of weaker nonlinearity exists in traditional assets. Additionally, the sensitivity to smaller events in bull markets is high for NFTs and DeFi. The findings have significant implications for portfolio diversification when an investor's portfolio set includes traditional assets and cryptocurrency and relatively new blockchain-based assets like NFTs and DeFi.
Research background: In order to examine market uncertainty, the paper depicts broad patterns of risk and systematic exposure to global equity market shocks for the major South Asian and Chinese equity markets, as well as for specific assets (gold and Bitcoin). Purpose of the article: The purpose of this paper is to investigate the dynamic correlation among the major South Asian equity markets (India and Pakistan), the Chinese equity markets, the MSCI developed markets, Bitcoin, and gold markets. Methods: While applying the GARCH-Vine-Copula model and the TVP-VAR Connectedness approach, major patterns of dependency and interconnectedness between these markets are investigated. Findings & value added: We find that risk shocks from developed equity markets are critical in these dynamic links. A net return spillover from Bitcoin to the Chinese and Pakistani stock markets throughout the sample period is reported. Interestingly, gold can be applied to hedge and diversify positions in China and major South Asian markets, particularly following the COVID-19 outbreak. Our paper presents three main original add valued: (1) This paper adds global factors to the targeted study of risk transmission among South Asian and Chinese stock markets for the first time. (2)The assets of Bitcoin and gold were added to the study of risk transmission among South Asian and Chinese stock markets for the first time, enabling the research in this paper to observe the non-linear link among the South Asian and Chinese stock markets with them. (3) Our research adds to these lines of inquiry by giving empirical evidence on how COVID-19 altered the dependent structure and return spillover dynamics of Bitcoin, gold and South Asian and Chinese stock markets for the first time. Our results have critical implications for investors and policymakers to effectively understand the nature of market forces and develop risk-averse strategies.
Masud Alam, Mohammad Ashraful Ferdous Chowdhury, Mohammad Abdullah, Mansur Masih
We investigate the return and volatility spillovers among NFTs, REITs, and other major financial assets from January 2019 to November 2022, using connectedness approaches. The findings indicate that total return and volatility connectedness increased during the COVID-19 and the RussiaâUkraine war. REITs partially maintained their historical independence from shocks from other assets, while NFTs emerged as the new portfolio diversifiers. Findings suggest that investors can use REITs or a combination of NFTs, OIL, GOLD, and REITs with other assets to hedge against volatile assets during periods of financial turmoil. These findings have significant implications for heterogeneous market participants aiming to identify optimal portfolio diversifiers.
The popularity of Bitcoin increased significantly in 2021. Bitcoin is considered to deliver high returns in a relatively short period, indicating that bitcoin has high volatility. Data with high volatility usually violates the Autoregresstive IntegratedinMovinginAverage (ARIMA)in homoscedasticity assumption. The Autoregressive Conditional Heteroscedasticity (ARCH) and General Autoregressive Conditional Heteroscedasticity (GARCH) model is often used to overcome the problem of heteroscedasticity in thelARIMA model. The ARCH and GARCH models canfbe used to model thefvolatilityfof data. This Research uses ARCH and GARCH models to overcome the heteroscedasticity problem caused by the high volatility of Bitcoin data for the period 30th June 2018 to 30th June 2022. The results of this study suggest that there might be a heteroscedasticity problem in Bitcoin data. The bestffiimodel for Bitcoin data ismiARIMA(1,0,[4])-GARCH(1,1) with an AIC value of -1,4263 at a 95% confidence level
Hohsuk Noh, Hyuna Jang, Kun Ho Kim, JongâMin Kim
This paper proposes a nonparametric directional dependence by using the local polynomial regression technique. With data generated from a bivariate copula having a nonmonotone regression structure, we show that our nonparametric directional dependence is superior to the copula directional dependence method in terms of the root-mean-square error. To validate the directional dependence with real data, we use the log returns of daily prices of Bitcoin, Ethereum, Ripple, and Stellar. We conclude that our nonparametric directional dependence, by using the local polynomial regression technique with asymmetric-threshold GARCH models for marginal distributions, detects the directional dependence better than the copula directional dependence method by an asymmetric GARCH model.
The cryptocurrency market is characterized by extremely high volatility. In the present study, we show the predictive ability of conditional EVT models in the cryptocurrency market during the price upsurge of 2020â2021. Taking high-frequency intraday data of four popular cryptocurrencies, Bitcoin, Ethereum, Litecoin, and Binance coin, we compare the accuracy of different competing models in estimating intraday value at risk (VaR) and expected shortfall (ES). The present study focuses on the extreme value theory (EVT) for modeling the tail of the distribution to forecast the measures of intraday VaR and ES. The study confirms the fat-tailed behavior of intraday returns of all four cryptocurrencies. Further, the study shows the magnitudes of high negative shocks are more than the positive ones for the returns of all four cryptocurrencies. The study uses suitable GARCH-family models such as apARCH, EGARCH, and CGARCH in the ARMA-GARCH framework. Using a two-stage approach the study shows how GARCH-EVT models with skewed studentâsâ t distribution outperform the predictability of conditional EVT with standard normal distribution as well as the unconditional EVT models in predicting intraday VaR and ES. The result of the study is useful for risk managers, day traders, and also for machine-based algorithmic trading.
Abstract This paper is motivated by Bitcoinâs rapid ascension into mainstream finance and recent evidence of a strong relationship between Bitcoin and US stock markets. It is also motivated by a lack of empirical studies on whether Bitcoin prices contain useful information for the volatility of US stock returns, particularly at the sectoral level of data. We specifically assess Bitcoin pricesâ ability to predict the volatility of US composite and sectoral stock indices using both in-sample and out-of-sample analyses over multiple forecast horizons, based on daily data from November 22, 2017, to December, 30, 2021. The findings show that Bitcoin prices have significant predictive power for US stock volatility, with an inverse relationship between Bitcoin prices and stock sector volatility. Regardless of the stock sectors or number of forecast horizons, the model that includes Bitcoin prices consistently outperforms the benchmark historical average model. These findings are independent of the volatility measure used. Using Bitcoin prices as a predictor yields higher economic gains. These findings emphasize the importance and utility of tracking Bitcoin prices when forecasting the volatility of US stock sectors, which is important for practitioners and policymakers.
This study provides a volatility estimation based on cross-market spreads by analyzing the behavior of Bitcoin cross-market arbitrageurs. This study crawls real-time price data from different exchanges for empirical analysis and verifies the accuracy and validity of the method employed by comparing it with the existing mainstream methods. The following conclusions are drawn: 1) The more exchanges that can be utilized, the smaller the Bitcoin price volatility, and the larger the cross-market spread, the better the estimation effect of the proposed method; and 2) Volume had no significant effect on the estimation using our method.
In this study, the RiskMetrics method is used to estimate Value at Risk for two exchange rates: BitCoin/dollar and the South African Rand/dollar. Value at Risk is used to compare the riskiness of the two currencies. This is to help South Africans and investors understand the risk they are taking by converting their savings/investments to BitCoin instead of the South African currency, the Rand. The Maximum Likelihood Estimation method is used to estimate the parameters of the models. Seven statistical error distributions, namely Normal Distribution, skewed Normal Distribution, Studentâs T-Distribution, skewed Studentâs T-Distribution, Generalized Error Distribution, skewed Generalized Error Distribution, and the Generalized Hyperbolic Distributions, were considered when modelling and estimating model parameters. Value at Risk estimates suggest that the BitCoin/dollar return averaging 0.035 and 0.055 per dollar invested at 95% and 99%, respectively, is riskier than the Rand/dollar return averaging 0.012 and 0.019 per dollar invested at 95% and 99%, respectively. Using the Kupiec test, RiskMetrics with Generalized Error Distribution (p > 0.07) and skewed Generalized Error Distribution (p > 0.62) gave the best fitting model in the estimation of Value at Risk for BitCoin/dollar and Rand/dollar, respectively. The RiskMetrics approach seems to perform better at higher than lower confidence levels, as evidenced by higher p-values from backtesting using the Kupiec test at 99% than at 95% levels of significance. These findings are also helpful for risk managers in estimating adequate risk-based capital requirements for the two currencies.
Danai Likitratcharoen, Pan Chudasring, Chakrin Pinmanee, Karawan Wiwattanalamphong
In recent years, the cryptocurrency market has been experiencing extreme market stress due to unexpected extreme events such as the COVID-19 pandemic, the Russia and Ukraine war, monetary policy uncertainty, and a collapse in the speculative bubble of the cryptocurrencies market. These events cause cryptocurrencies to exhibit higher market risk. As a result, a risk model can lose its accuracy according to the rapid changes in risk levels. Value-at-risk (VaR) is a widely used risk measurement tool that can be applied to various types of assets. In this study, the efficacy of three value-at-risk (VaR) modelsânamely, Historical Simulation VaR, Delta Normal VaR, and Monte Carlo Simulation VaRâin predicting market stress in the cryptocurrency market was examined. The sample consisted of popular cryptocurrencies such as Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Cardano (ADA), and Ripple (XRP). Backtesting was performed using Kupiecâs POF test, Kupiecâs TUFF test, Independence test, and Christoffersenâs Interval Forecast test. The results indicate that the Historical Simulation VaR model was the most appropriate model for the cryptocurrency market, as it demonstrated the lowest rejections. Conversely, the Delta Normal VaR and Monte Carlo Simulation VaR models consistently overestimated risk at confidence levels of 95% and 90%, respectively. Despite these results, both models were found to exhibit comparable robustness to the Historical Simulation VaR model.
The paper examines whether an unanticipated event like the COVID-19 crisis has strengthened the contagion in the cryptocurrency market utilizing samples of data representing the pre-crisis and post-crisis periods. Employing the wavelet coherence and DCC-GARCH(1,1) models, we identify that the cryptocurrency market started integrating from 2018 as volatility within the market reduced. Our main finding is that the cryptocurrency market is highly interconnected and that the contagion strengthened during the crisis period. We draw appropriate policy implications from these findings.
This chapter scrutinizes the dynamic linkages between major cryptocurrencies and fiat currencies of developed and emerging countries. To do this, the authors estimate the Scalar-BEKK GARCH models from September 2017 to January 2022. To shed light on the effects of specific events, the authors also estimate the models for the sub-periods: the great crypto crash, the Covid-19 pandemic, and the vaccination. Empirical results suggest that the time-varying relationships between the crypto- and fiat currencies highly depend on the country- and crypto-specific dynamics. By the decentralized nature of cryptocurrencies, it is not an easy venture to define the stylized facts on those dynamic relationships. The most striking result shows a sharp and massive decline in the conditional covariances between the cryptos and the fiat currencies of developed countries except the Japanese Yen at the onset of the Covid-19 pandemic.
The intensity of volatility persistence is sensitive to time scales, market returns and data regimes. Investors who acquire intangible digital assets in the form of "cryptocurrencies" should consider that they may or may not receive a fiat currency. Sometimes there is a possibility of a loss of the entire investment due to volatility of prices in digital currency/cryptocurrency. Several empirical studies are conducted to measure the volatility behavior of cryptocurrencies using different mathematical models like: i) Autoregressive Distributed Lag (ARDL) Model, ii) Heterogeneous Autoregressive (HAR) Model, iii) Autoregressive Conditional Heteroskedasticity (ARCH) Model, and iv) Generalized Autoregressive Conditional Heteroscedastic (GARCH) Models. This paper focuses on the review of various GARCH Models studied during 1980-2020.
This paper discusses whether the Bitcoin exchange-traded fund (ETF), which tracks the value of Bitcoin, improves equity portfolios, by using a robust portfolio performance analysis. The equity portfolio is represented by an ETF that tracks the Standard & Poorâs 500. We use data from a turbulent investment period within the coronavirus pandemic, to study the diversification benefits of Bitcoin. We compare the performances of diverse portfolios composed of both ETFs, which include 40 classical dynamic volatility model-based portfolios and 900 score-driven portfolios. For the score-driven portfolios, the dynamic association is modelled by score-driven Clayton, rotated Clayton, Gumbel, rotated Gumbel and Studentâs t copulas. We compare portfolio strategies using the model confidence set test. We find that score-driven portfolios outperform classical volatility model-based portfolios and the equity portfolio. Our results may provide suggestions for cryptocurrency investors on portfolio optimization and may also have policy implications for regulators and policymakers.
This study conducted the econometric analysis to test the hedge and safe haven effects of Non-fungible Tokens (NFTs) on major traditional asset markets in the global financial system. We investigate the estimates of these effects in times of extreme market conditions and the COVID-19 crisis. Our empirical results show evidence of the hedge and safe haven properties of NFTs, confirming two main findings: (i) NFTs act as a hedge and safe haven for particular stock markets and oil, bond, and USD indices, even though the degree of effects varies across asset classes; and (ii) NFTs also serve as sheltering facilities for the markets mentioned above, with more substantial safe haven benefits for bond and USD indices during the recent pandemic crisis.