Financial markets, particularly cryptocurrency markets, are characterized by high volatility and sudden price jumps, making it essential to develop models that can capture these dynamics effectively. In this paper, our focus lies on the Merton’s jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of methodologies. We adopt an approach that involves implementing different drift, volatility, and jump terms within the model through various machine learning techniques, traditional methods, and statistical methods on price-volume data. Additionally, we introduce a path-dependent Monte Carlo simulation to model cryptocurrency prices, taking into account the volatility and unexpected jumps in prices. The results indicate that incorporating jump processes significantly improves forecasting accuracy, especially in volatile markets. Our findings highlight the effectiveness of combining machine learning and traditional methods for more robust predictions.
Yiming Zhao, Sultan Salem, Areej M. AL-Zaydi, Jin-Taek Seong · 6 authors
Among the different financial sectors, the modeling and forecasting of log-returns of cryptocurrency have received considerable attention. Numerous statistical models have been put forward to analyze the log returns of the cryptocurrency. However, as per our knowingness and immense literature search, we did not find published shreds of evidence about modeling cryptocurrency's log-returns while manipulating trigonometric-based statistical models. This paper provides a worthwhile endeavor to fill out this amusing research gap by manipulating a new trigonometric-based statistical methodology called the generalized sine-G family. Utilizing the generalized sine-G, a statistical model called the generalized sine-Logistic distribution is introduced. The generalized sine-Logistic distribution is applied for modeling the log-returns of two cryptocurrencies. Using certain decisive tools, it is observed that the generalized sine-Logistic is the best-suited distribution for modeling the given log-returns data sets. Additionally, this study uses various sophisticated and robust econometric techniques, such as the Least Absolute Shrinkage and Subset Selection, Markov Switching Generalized Autoregressive Conditional Heteroscedasticity (MSGARCH), and Step Indicator Saturation (SIS) model with different distributions, to predict (in-sample) the log-returns data sets. The effectiveness of each method is assessed through a popular loss function known as the root-mean-square error (RMSE).
We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and liquidity diffusion, which capture magnitude and volatility of liquidity fluctuation, respectively, and construct liquidity-adjusted return and volatility that reflect real-time liquidity variability. These liquidity-adjusted inputs are integrated into a VECM-DCC/ADCC-Bayesian model, allowing for conditional and posterior covariance estimation under liquidity stress. Applying this framework to portfolios of cryptocurrencies and US stocks, we find that traditional models misrepresent volatility and co-movement, while liquidity-adjusted models yield more stable and interpretable risk structures, particularly for portfolios of cryptocurrencies. The findings support the use of liquidity-adjusted multivariate models as statistically grounded tools for assessing the propagation of portfolio risk under market frictions, with implications for asset pricing, market microstructure design, and portfolio management.
Abstract The main objective of this study is to investigate tail risk connectedness among six major cryptocurrency markets and determine the extent to which investor sentiment, economic conditions, and economic uncertainty can predict tail risk interconnectedness. Combining the Conditional Autoregressive Value-at-Risk (CAViaR) model with the time-varying parameter vector autoregressive (TVP-VAR) approach shows that the transmission of tail risks among cryptocurrencies changes dynamically over time. During crises and significant events, transmission bursts and tail risks change. Based on both in- and out-of-sample forecasts, we find that the information contained in investor sentiment, economic conditions, and uncertainty includes significant predictive content about the tail risk connectedness of cryptocurrencies.
Praise Otito Obanya, Modisane Seitshiro, Carel P. Olivier, Tanja Verster
Cryptocurrencies are widely regarded as volatile and less predictable assets by financial participants. The behaviour and dynamics of Bitcoin’s daily volatility, obtained by fitting GARCH models, are investigated for a period of 8 years using permutation entropy which is represented by the variable H for calculations. The best fitting GARCH models selected are the FIGARCH(1,0.7,1) and SGARCH(1,1) models based on maximum likelihood estimation, Akaike Information Criterion and Bayesian Information Criterion. Simulated volatilities are also obtained from the best fitting GARCH models using their respective parameters, to confirm how well the models fit. The results obtained show that the H values of Bitcoin are generally low and that the dynamics of Bitcoin’s volatility is quite predictable, as Bitcoin’s volatility is most likely to decline over time than increase or have an alternating movement. Also, the simulated volatilities show good agreement with the real-world volatility, confirming the models as good fits.
Yaoyue Tang, Karina Arias-Calluari, M. N. Najafi, Michael Harré · 5 authors
This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.
Cryptocurrencies have become a popular investment option and the Ethereum has become a mainstream cryptocurrency because of the additional functionality that can be accomplished with the backing of the powerful Ethereum network compared to Bitcoin. The high volatility of Ethereum offers both profits and risks, making it crucial to improve the forecasting ability for its price volatility. The results of this study could be useful for investors and policymakers who are interested in understanding and managing the risks associated with investing in Ethereum. Several studies have explored similar topics using heterogeneous autoregressive (HAR) models for cryptocurrencies, but this paper offers a more expansive approach. This paper employs five-minute high-frequency data to construct 4 HAR models to predict the volatility of Ethereum, taking into account the impact of structural breaks, Bitcoin, SP500 and VIX. The model that considers all factors outperforms other models for out-of-sample predictions for the 1-week forecasting. Due to the nature of the Ethereum price, the HAR-RV model has achieved a perfect fit in 1-day and 1-month forecasting. Therefore, other models have a very small improvement in fitness and prediction accuracy. This paper contributes to the understanding of Ethereum’s volatility and its impact on the cryptocurrency market.
Tonuchi E. Joseph, Atif Jahanger, Joshua Chukwuma Onwe, Daniel Balsalobre‐Lorente
Abstract This study examined the interconnectedness and volatility correlation between cryptocurrency and traditional financial markets in the five largest African countries, addressing concerns about potential spillover effects, especially the high volatility and lack of regulation in the cryptocurrency market. The study employed both diagonal BEKK-GARCH and DCC-GARCH to analyze the existence of spillover effects and correlation between both markets. A daily time series dataset from January 1, 2017, to December 31, 2021, was employed to analyze the contagion effect. Our findings reveal a significant spillover effect from cryptocurrency to the African traditional financial market; however, the percentage spillover effect is still low but growing. Specifically, evidence is insufficient to suggest a spillover effect from cryptocurrency to Egypt and Morocco’s financial markets, at least in the short run. Evidence in South Africa, Nigeria, and Kenya indicates a moderate but growing spillover effect from cryptocurrency to the financial market. Similarly, we found no evidence of a spillover effect from the African financial market to the cryptocurrency market. The conditional correlation result from the DCC-GARCH revealed a positive low to moderate correlation between cryptocurrency volatility and the African financial market. Specifically, the DCC-GARCH revealed a greater integration in both markets, especially in the long run. The findings have policy implications for financial regulators concerning the dynamics of both markets and for investors interested in portfolio diversification within the two markets.
Mario Iván Contreras-Valdez, Sonal Sahu, José Antonio Núñez Mora, Roberto J. Santillán‐Salgado
In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning between 1 January 2017 and 25 October 2022, with a primary focus on Bitcoin and Ethereum, our research seeks to accentuate the resilience of VaR methodology as a paramount risk assessment tool. The essence of our investigation lies in advancing the comprehension of VaR accuracy by quantitatively comparing the observed returns of both cryptocurrencies with their corresponding estimated values, with a central theme being the endorsement of the Normal Inverse Gaussian distribution as a potent model for risk measurement, particularly in the domain of high-frequency data. To bolster the statistical reliability of our results, we adopt a forward test methodology, showcasing not only a contribution to the evolution of risk assessment techniques in Finance but also underscoring the practicality of sophisticated distributional models in econometrics. Our findings not only contribute to the refinement of risk assessment methods but also highlight the applicability of such models in precisely modeling and forecasting financial risk within the dynamic realm of cryptocurrencies, epitomized by the case study of Bitcoin and Ethereum.
Virginie Terraza, Aslı Boru, Mohammad Mahdi Rounaghi
Abstract The spread of the coronavirus has reduced the value of stock indexes, depressed energy and metals commodities prices including oil, and caused instability in financial markets around the world. Due to this situation, investors should consider investing in more secure assets, such as real estate property, cash, gold, and crypto assets. In recent years, among secure assets, cryptoassets are gaining more attention than traditional investments. This study compares the Bitcoin market, the gold market, and American stock indexes (S&P500, Nasdaq, and Dow Jones) before and during the COVID-19 pandemic. For this purpose, the dynamic conditional correlation exponential generalized autoregressive conditional heteroskedasticity model was used to estimate the DCC coefficient and compare this model with the artificial neural network approach to predict volatility of these markets. Our empirical findings showed a substantial dynamic conditional correlation between Bitcoin, gold, and stock markets. In particular, we observed that Bitcoin offered better diversification opportunities to reduce risks in key stock markets during the COVID-19 period. This paper provides practical impacts on risk management and portfolio diversification.
Dennis Koch, Vahidin Jeleskovic, Zahid Irshad Younas
This paper introduces a unique and valuable research design aimed at analyzing Bitcoin price volatility. To achieve this, a range of models from the Markov Switching-GARCH and Stochastic Autoregressive Volatility (SARV) model classes are considered and their out-of-sample forecasting performance is thoroughly examined. The paper provides insights into the rationale behind the recommendation for a two-stage estimation approach, emphasizing the separate estimation of coefficients in the mean and variance equations. The results presented in this paper indicate that Stochastic Volatility models, particularly SARV models, outperform MS-GARCH models in forecasting Bitcoin price volatility. Moreover, the study suggests that in certain situations, persistent simple GARCH models may even outperform Markov-Switching GARCH models in predicting the variance of Bitcoin log returns. These findings offer valuable guidance for risk management experts, highlighting the potential advantages of SARV models in managing and forecasting Bitcoin price volatility.
The article “Systematic Hedging of the Cryptocurrency Portfolio” on QuantPedia discusses a strategy for hedging a cryptocurrency portfolio that is stored in cold storage The article suggests that while cold storage has advantages, such as protection against hacking, it also exposes the holder to the price swings of the cryptocurrency market. The article proposes a hypothetical market capitalization-weighted Top 5 cryptocurrency index portfolio (T5) as a proxy for a portfolio that hardcore HODLers may hold. The rule for inclusion in the index is simple: each year, on the first day of the year, select the top 5 coins ranked by market cap for a yearly holding period. Stablecoins are excluded from the index. The article then explores a hedging strategy through BTC derivatives to minimize crypto market beta exposure risk. One approach introduced is a 1:1 (Proportional) Hedge, where the exact amount of $ value corresponding to Bitcoin (BTC) is shorted. The article suggests that this strategy can help mitigate the risk of price swings in the cryptocurrency market, especially when the market is at an all-time high. Please note that this is a high-level summary and for a detailed understanding, you should read the full article.
The main goal of the research is to predict the future monthly returns of cryptocurrencies using the Vector Error Correction Model (VECM). Time series for the period 2018-2021 consists o f data on monthly returns for the cryptocurrencies Bitcoin, Ethereum and Ripple, as well as monthly returns on gold and the S&P500 stock index. Within the VECM, using the Johansen and Granger tests, short-term cointegration and causality among variables were determined, without the existence o f long-term equilibrium. The resulting model for short-term prediction o f the monthly returns o f the cryptocurrency Bitcoin was evaluated as unbiased and stable with a realistic forecast error o f 0.168 (16.8%).
Alexia Anastasopoulos, Nikola Gradojević, Fred Liu, Alex Maynard · 5 authors
We assess the information content of order flow for the cross-section of cryptocurrency returns. Our analysis is based on a set of international order flows denominated in 11 major currencies that reflect world order flow. We find that world order flow has strong explanatory and predictive power for cryptocurrency returns. Order flow tends to dominate economic fundamentals for out-of-sample prediction, especially in the context of non-linear machine learning models, and its performance cannot be explained by limits to arbitrage. Overall, our findings indicate that order flow has a permanent effect on cryptocurrency returns.
Abstract This study examines how global geopolitical risks , threats , and acts impact the daily returns of 10 major cryptocurrencies (BTC, ETH, USDT, XRP, BNB, USDC, BCH, DOGE, LTC, and ADA). The statistically significant results that are robust to the consideration of alternative model specifications and control variables suggest that there is strong evidence for (i) ETH, XRP, BNB and BCH responding negatively to the shocks of geopolitical risks , (ii) BTC, ETH, BNB, BCH, LTC and ADA responding negatively to the shocks of geopolitical threats , and (iii) all 10 cryptocurrencies not responding to the shocks of geopolitical acts . As these 10 cryptocurrencies do not respond positively to any of the three shocks in a robust and statistically significant way either, it is implied that none of them offer a reliable hedge against geopolitical risks.
The growing interest in cryptocurrencies has drawn the attention of the financial world to this innovative medium of exchange. This study aims to explore the impact of cryptocurrencies on portfolio performance. We conduct our analysis retrospectively, assessing the performance achieved within a specific time frame by three distinct portfolios: one consisting solely of equities, bonds, and commodities; another composed exclusively of cryptocurrencies; and a third, which combines both 'traditional' assets and the best-performing cryptocurrency from the second portfolio.To achieve this, we employ the classic variance-covariance approach, utilizing the GARCH-Copula and GARCH-Vine Copula methods to calculate the risk structure. The optimal asset weights within the optimized portfolios are determined through the Markowitz optimization problem. Our analysis predominantly reveals that the portfolio comprising both cryptocurrency and traditional assets exhibits a higher Sharpe ratio from a retrospective viewpoint and demonstrates more stable performances from a prospective perspective. We also provide an explanation for our choice of portfolio optimization based on the Markowitz approach rather than CVaR and ES.
The World Health Organization (WHO) announced the Covid-19 pandemic in March 2020, which had a negative impact on economic activities and financial markets. Cryptocurrencies with blockchain technology, whose history is not old, took off in the Covid-19 period thanks to digital transformation and became popular in the financial markets. However, the fact that cryptocurrencies lose blood after the pandemic period. This study examines the volatility of cryptocurrencies before, during and after the pandemic Covid-19 using data from 4 cryptocurrencies (Bitcoin, Ethereum, Binance and Litecoin) and the CCI30 index, using autoregressive conditional variance models with two dummy variables. According to the results, the volatility of cryptocurrencies decreases throughout the pandemic period, moreover, decreases more after the pandemic compared to the pre-pandemic period. Investors should be cautious about investing in these risky instruments, which may become popular again in the future, just in case.