Abstract The emergence of cryptocurrencies has presented investors with novel portfolio diversification opportunities. This study investigates the interplay between precious metals and cryptocurrencies, examining their potential for enhancing portfolio returns and mitigating risk. Using daily closing prices from August 2017 to November 2022, we employ an autoregressive distributed lag (ARDL) approach to analyze comovement and causality between these asset classes. Our findings reveal a short-run linkage between Bitcoin, precious metals, and other cryptocurrencies but no long-run cointegration. Notably, gold prices unidirectionally influence cryptocurrency prices, a relationship not observed with other assets. This absence of long-term comovement suggests that precious metal investors can leverage modern portfolio theory to diversify cryptocurrency volatility risk. These results offer valuable insights for investors seeking to optimize portfolios by strategically incorporating cryptocurrencies for improved risk-adjusted returns.
Dwi Fitrizal Salim, Farida Titik Kristanti, Hosam Alden Riyadh, Mailinda Tri Wahyuni
Type of the article: Research ArticleAbstractThis study evaluates and compares risk measurement models for ten major cryptocurrencies: Bitcoin, Ethereum, Tether, Ripple, Dogecoin, Cardano, Binance Coin, Polkadot, Solana, and USD Coin. Using daily log-return data from January 2017 to October 2024, the analysis applies Modified Cornish-Fisher Value-at-Risk and standard, exponential, threshold, and Markov-switching generalized autoregressive conditional heteroskedasticity models. The main comparison is conducted at the 99% confidence level, while model reliability is assessed through out-of-sample backtesting using 500 observations and the Kupiec unconditional coverage and Christoffersen conditional coverage tests. The results reveal substantial heterogeneity in cryptocurrency risk. Modified Cornish-Fisher Value-at-Risk produces highly sensitive estimates for assets with extreme skewness and kurtosis, particularly Ripple, Cardano, and Dogecoin. However, no single model performs consistently better across all assets. Bitcoin is the only cryptocurrency for which all tested models pass both backtesting procedures. The Markov-switching specification provides acceptable coverage for Bitcoin, Ripple, and Dogecoin but does not consistently outperform conventional volatility models. Standard and asymmetric volatility models provide stronger support for Cardano, Binance Coin, and Polkadot, whereas Ethereum, Solana, and USD Coin remain difficult to model under the examined specifications. These findings demonstrate that cryptocurrency risk measurement requires asset-specific model selection based on both estimated loss magnitude and formal backtesting evidence.
Fernando Henrique Antunes de Araujo, Milena Kojić, Petar Mitić, Kerolly Kedma Felix do Nascimento · 5 authors
This study applies a prespecified dynamic MFDFA workflow across pandemic, geopolitical-conflict, and tariff-policy regimes for ten non-stable, long-history cryptoassets selected ex post from the 23 July 2026 market-cap ranking. The common sample comprises 3155 daily log returns per asset from 2 December 2017 to 22 July 2026; the final endpoint regime includes the U.S.–Iran conflict. The estimator uses q=−10,−8,…,10, linear detrending, 22 scales from 16 to N10, adjacent-secant Legendre transformation, a cubic spectrum peak, and 500-day windows stepped by 21 days plus a terminal endpoint. Full-sample IE=|α0−0.5| ranges from 0.01397 (LINK) to 0.08706 (BNB), and observed width ranges from 0.32625 to 0.74678. The controlled incremental U.S.–Iran endpoint coefficient is −0.02734 (two-way clustered SE 0.02369; p=0.2489), with asset-cluster t(9) interval [−0.08226, 0.02759]. Quantile estimates range from +0.00206 at the 0.10 quantile to −0.04769 at the 0.90 quantile; all five 999-replication asset-cluster bootstrap percentile intervals include zero. Exact rolling sensitivities are negative for the 500/14, 500/30, and 730/30 designs but positive for the 250/21 design, and every small-cluster interval includes zero. Direct spectrum-width contrasts also remain nonsignificant after Holm adjustment. None of ten observed widths survives BH correction in 200 shuffled-return surrogates per asset (2000 fits in total). The results document heterogeneous and specification-sensitive dynamic multifractal patterns, not isolated or causal crisis effects.
This paper selects the data of Bitcoin, Gold, and the S&P 500 index from 2018 to 2025, utilizing GARCH(1,1) and DCC-GARCH models to depict the dynamic conditional correlations among assets. By incorporating the Global Geopolitical Risk Index, the 10-year breakeven inflation rate, and the VIX panic index, it constructs daily and monthly cross-frequency regression models to examine their macro-driving mechanisms. The results show that whether at the high-frequency daily level or the smoothed monthly level, macroeconomic variables exhibit extremely significant driving effects on the co-movement of Bitcoin. Under the liquidity squeeze concerns triggered by intensified global panic or high inflation expectations, Bitcoin fails to act as a haven alongside gold. Instead, it exhibits a stronger synchronous crash with the US stock market. This empirical study rejects the hypothesis of Bitcoin as "digital gold," revealing its essence as a "risk amplifier" highly dependent on traditional liquidity, and provides quantitative support for international investors in asset allocation under extreme macroeconomic scenarios.
Cryptocurrency time-series forecasting is a challenging task because market data usually exhibit high noise, strong volatility, non-stationarity, nonlinear dynamics, and long-range dependencies. In addition, multivariate market indicators often contain redundant or weakly informative variables, which may reduce forecasting accuracy and model interpretability. To address these issues, this study proposes BSFinformer, a Boruta-SHAP enhanced Finformer framework for multivariate cryptocurrency time-series forecasting. The proposed framework first applies a leakage-aware Boruta-SHAP feature selection strategy to identify informative market variables and remove redundant features. To avoid temporal information leakage, feature selection is performed only on the training set, and the selected feature subset is then applied unchanged to the validation and test sets. The selected features are subsequently fed into an improved Finformer model that integrates temporal embedding, sequence decomposition, and sparse self-attention to capture local fluctuations, trend evolution, and long-range temporal dependencies. Experiments are conducted on three cryptocurrency assets, namely Bitcoin, Dogecoin, and Binance Coin, using chronological train–validation–test splits. The proposed model is compared with classical forecasting models and recent long-sequence forecasting baselines, including LSTM, Transformer, Informer, Autoformer, DLinear, PatchTST, TimesNet, and iTransformer. Experimental results show that BSFinformer achieves competitive forecasting performance in terms of MSE and MAE. Ablation experiments further demonstrate the contributions of Boruta-SHAP feature selection, temporal embedding, sequence decomposition, and sparse self-attention. These results indicate that feature-selected temporal modeling can improve forecasting accuracy and interpretability for multivariate cryptocurrency market data.
The fluctuation characteristics of financial time series have always been one of the research hotspots in the academic community. Generally speaking, financial return series have the characteristics of volatility clustering, fat tails, conditional heteroskedasticity, asymmetric shocks, etc. The above phenomena can be explained from the perspective of dynamic conditional variance by GARCH models and their extensions. This paper first introduces the basic ideas of ARCH and GARCH models, with a focus on the issue of volatility clustering of financial returns. Then, it reviews the relevant research from three aspects: model evolution, application scenarios, and practical value. It also analyzes the role of GARCH-type models in capturing volatility persistence, asymmetric impact, and risk transmission through applications in cryptocurrencies, energy assets, and high-frequency financial data. The study shows that GARCH-type models capture the volatility clustering feature of financial returns well, but there is still room to improve the modeling of extreme risk, the handling of high-dimensional assets, and model interpretability.
Volatility control converts risk estimates into portfolio exposure, yet existing approaches often rely on a fixed volatility estimator or a pre-defined control rule that may not adapt to changing market conditions. We propose VolRouter, a modular framework that formulates volatility control as state-conditioned routing over estimator-controller pairs. VolRouter first summarizes market conditions into a control-relevant state profile and then performs routing through three stages: state inference, switch review, and pair selection. The Router can be implemented using rule-based, learnable, or LLM-based decision modules, while portfolio actions remain generated by predefined control policies. We evaluate VolRouter across S&P 500, Multi-Asset, Bitcoin, and USDT volatility-control settings. VolRouter achieves the highest Sharpe ratio in three of four settings. On S&P 500, it improves Sharpe from 0.952 for RV + Naive Scaling to 1.222 while reducing maximum drawdown from 15.10% to 12.58% and daily CVaR from 1.76% to 1.32%. On Multi-Asset, it improves Sharpe from 1.498 to 1.540 and reduces CVaR from 1.56% to 1.18%. Bitcoin shows similar improvements in risk-adjusted performance, while USDT provides a boundary case where simpler state-aware selectors remain competitive. Ablation and sensitivity analyses show that the improvement comes from relative policy evaluation and selective persistent switching rather than simply expanding the policy library. These results suggest that volatility control can be viewed as a policy-selection problem when risk management requirements vary across market states.
With the improvement of data technology advances and the sharp addition of web customers number since the 90s, numerous computerized monetary standards are presented. the most popular among them is Bitcoin. It was decided to investigate the possible relations between the most popular cryptocurrency Bitcoin price dynamics and global Nasdaq index dynamics using Mathematical and Statistical methods. The main question is: Are the Bitcoin prices somehow related with Nasdaq Composite Index? We use both, Quantitative and Qualitative data analysis methods to answer this question: Namely, the Regression model and Non-Parametric testing. According to Quantitative methods, it was found that there exists a correlation and the regression equation is not bed: it seems that it is possible to explain about 60% of changes in Bitcoin Prices by changes in the Nasdaq Index. According to Qualitative methods, it was found that these two variables are independent. In this case, the Qualitative conclusion is more likely to be right, and the correlation is most likely because of coincidence.
This study investigates two questions relating to cryptocurrency market dynamics. First, whether a composite skew measure derived from MicroStrategy (MSTR) trading activity can predict future Bitcoin (BTC) and Ethereum (ETH) volatility. Second, whether Ethereum volatility exhibits reproducible structural properties consistent with established theories of volatility persistence and cascading shock dynamics. Using rolling out-of-sample testing, autocorrelation-adjusted significance testing, regime classification, shock-decay modelling, return-interval analysis, and earthquake-inspired cascade frameworks, the study finds no evidence that MSTR composite skew provides a useful forecasting signal. More broadly, no forecasting model tested outperforms naive benchmark models beyond horizons of approximately three to five days. However, several descriptive properties of Ethereum volatility appear robust, including volatility persistence, regime structure, extreme-event clustering, non-simple shock decay, and partially transferable aftershock dynamics. In particular, while Omori-style decay and the productivity law are supported, Bath's Law fails consistently, suggesting cryptocurrency volatility cascades may differ fundamentally from those observed in traditional financial markets. The findings contribute to the understanding of volatility organisation in digital asset markets while highlighting the difficulty of extracting persistent predictive signals from historical OHLCV
This paper investigates the evolving link between cryptocurrency and equity markets in the context of the recent wave of corporate Bitcoin (BTC) treasury strategies. We assemble a dataset of 39 publicly listed firms holding BTC, from their first acquisition through April 2025. Using daily logarithmic returns, we first document significant positive co-movements via Pearson correlations and single factor model regressions, discovering an average BTC beta of 0.62, and isolating 12 companies, including Strategy (formerly MicroStrategy, MSTR), exhibiting a beta exceeding 1. We then classify firms into three groups reflecting their exposure to BTC, liquidity, and return co-movements. We use transfer entropy (TE) to capture the direction of information flow over time. Transfer entropy analysis consistently identifies BTC as the dominant information driver, with brief, announcement-driven feedback from stocks to BTC during major financial events. Our results highlight the critical need for dynamic hedging ratios that adapt to shifting information flows. These findings provide important insights for investors and managers regarding risk management and portfolio diversification in a period of growing integration of digital assets into corporate treasuries.
Gouher Ahmed, Hamza Naim, Aqila Rafiuddin, Mohammed Nizamuddin · 5 authors
This study deals with the performance analysis and volatility estimation of conventional indices including Dow Jones, S&P 500, Brent Oil, Crude Oil and Gold and cryptocurrencies including Bitcoin and Ethereum for the period January 3, 2011 to November 26, 2021 for all of the indices except Ethereum for which the period chosen was from March 10, 2016 to November 26, 2021 due to late incorporation of the cryptocurrency. The stationarity, heteroscedasticity, and serial correlation of the data were considered. Time series regression using the GARCH model is applied for performance analysis and volatility estimation. GARCH (1, 1) estimates show the high performance of cryptocurrencies over the conventional indices, except Gold, which was insignificant, with Ethereum followed by Bitcoin being the most volatile among the different indices. However, Gold remains inert in response to the different indices. However, although the cryptocurrencies add to the country’s revenue, thus minimizing the deficits, there should still be proactive policies and practices to prevent the exploitation of stakeholders, especially for the sake of minority ones.
Francesco Cesarone, Gianna Figà‐Talamanca, Francesca Luciani
Abstract This study develops a large-scale framework to evaluate whether, and under what conditions, adding cryptocurrencies to equity investment universes improves portfolio performance.We apply four long-only portfolio strategies, Global Minimum Variance, Risk Parity, Most Diversified Portfolio, and Equally Weighted, to 10,000 randomly generated investment universes. These universes consist of baskets containing either only equities or varying combinations of equities and cryptocurrencies. We conduct an out-of-sample analysis on real-world data from 2018 to 2023 to assess the influence of cryptocurrencies on portfolio outcomes. The empirical findings reveal that portfolios constructed from mixed equity and cryptocurrency universes provide a better risk-return profile compared to purely equity-based portfolios, particularly for Risk Parity, Most Diversified, and Equally Weighted.
Aktam U. Burkhanov, Abdul Jalil Mahama, Ilyоs Abdullaev, Nodira B. Abdusalomova · 6 authors
Type of the article: Research ArticleAbstractStablecoins serve as the primary liquidity and settlement platform for decentralized finance, yet recent market shocks and de-pegging events demonstrate systemic vulnerability regarding their stability. The purpose of this study is to quantify the tail risk of Tether (USDT) to determine the accuracy of different risk modeling frameworks during periods of extreme market stress. This study employs historical simulation, parametric Gaussian models, Monte Carlo simulation, and Extreme Value Theory using the Peaks-Over-Threshold approach on daily log returns from 2015 to 2025. Statistical diagnostics confirm high excess kurtosis of 24.3 and a negative skewness of –3.1 in the asset returns, which explicitly invalidates normal distribution assumptions. The empirical results reveal that Gaussian methods systematically underestimate extreme risk by 47% during high-volatility regimes. Extreme Value Theory models capture fat-tailed behavior with 50% higher precision than traditional models, identifying a maximum potential one-day loss of 1.50%. Backtesting parameters at the 95% and 99% confidence levels show that standard Value at Risk models fail to predict 14 out of 18 historical tail-risk anomalies. Expected Shortfall calculations under the generalized Pareto distribution successfully cover 99.8% of historical volatility spikes. This study concludes that Extreme Value Theory frameworks are essential for the robust design of decentralized finance protocols and the development of institutional risk management standards.AcknowledgmentsThe authors express gratitude to our respective university departments and institutional research groups for providing the technical infrastructure necessary to conduct this study. We also recognize the participants of internal research seminars whose early feedback helped refine the core empirical parameters of this stablecoin risk framework.
Daniel Pereira Alves de Abreu, Octávio Valente Campos, Aureliano Angel Bressan
Objective: This study aims to evaluate the performance of different ARMA-GARCH model specifications in the risk management of major cryptocurrencies, investigating whether the inclusion of exogenous variables improves the calibration of risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). Methodology: To achieve this objective, 4,032 specifications of the ARMA-GARCH model applied to the ten main cryptocurrencies in trading were tested. The study incorporated the Fear and Greed Index and Bitcoin Trading Volume as exogenous variables in an ARMA-GARCH-X framework, comparing the performance of the different specifications against an ARMA(1,1)-GARCH(1,1) benchmark. Originality: Despite growing interest in crypto asset risk management, there are still gaps in the literature regarding the effectiveness of incorporating exogenous variables into forecasting models, as well as the increase in the quality of forecasts when using more complex models. Main results: The results indicate that the inclusion of external variables improves risk calibration in some assets, although the gains are marginal and heterogeneous. There is also no single optimal parameterization, requiring ARMA orders, GARCH specifications, and error distributions to be adjusted for each cryptocurrency. Theoretical/methodological contributions: From a methodological point of view, the study contributes by demonstrating the importance of specific calibration of ARMA-GARCH models for different cryptocurrencies in risk estimation. Furthermore, the results suggest that, although more complex models can improve tail risk estimation, the gains in predictive power over simpler models are limited. Keywords: Cryptocurrencies; Risk Management; ARMA-GARCH; Value-at-Risk; Expected Shortfall.
The purpose of this study is to examine the potential safe-have properties of the two most popular cryptocurrencies, i.e., Bitcoin and Ethereum, against equites, government bonds and gold. To do so, the paper makes use of a daily dataset ranging from 2018 to 2022 acknowledging both the COVID-19 and the potential halving effect in the cryptocurrency market. To robustly assess the research question, the paper employs a quantile GARCH model with non-parametric diagnostics, dynamic Local Projections and rolling window estimations for robustness. The findings of the paper suggest that both assets act as diversifiers against equities and against each other, whereas the halving effect is statistically insignificant and the COVID-19 effect is statistically significantly positive only for the returns of Ethereum. The results imply that cryptocurrencies could contribute to portfolio diversification under stress market conditions.
The paper examines the volatility spillover effects and long-term relationship between cryptocurrencies and traditional financial markets in Türkiye using BEKK-GARCH and DCC-GARCH models. It analyses the perception of crypto assets as a “digital safe haven” in an economy marked by high inflation, exchange rate fragility, and financial uncertainty. Using monthly price data for Bitcoin, Ethereum, BIST-100, and Republic Gold from January 2010 to February 2025, the study applies unit root tests, Johansen cointegration, ARDL bounds, and Engle-Granger tests. Results show no long-term price cointegration, but Bitcoin and Ethereum returns are strongly correlated, with DCC-GARCH results showing a dynamic correlation above 50%, while gold and BIST-100 correlate weakly or negatively. BEKK-GARCH highlights significant volatility transmission from Bitcoin to Ethereum, with BIST-100 maintaining persistent volatility. The study concludes that crypto and traditional markets in Türkiye are not integrated long-term, but short-term interactions exist at the return level, with implications for portfolio diversification and financial stability.
Drissia Ennagoura, Kamal El Kehal, Safae Merzouk, BERDAI ABDELHAMID · 8 authors
Prices of cryptocurrencies are tough to forecast due to their high volatility and susceptibility to abrupt market changes. This paper compares four models—ARIMA, Prophet, LSTM, and XGBoost—to predict Ethereum (ETH) prices on three horizons: 15 minutes, 1 hour, and 1 day. We compared all four models concerning Root Mean Squared Error (RMSE) from the historical ETH data. The outcome shows XGBoost performs best on short-term forecasting with an RMSE of 352 in 15-minute and 357 in 1-hour data, surpassing LSTM and ARIMA. For the daily prediction, Prophet shows competitive performance with an RMSE of 941, whereas ARIMA is generally stable. The findings conclude that the ideal model depends on the forecasting horizon, and for short-term trading, using XGBoost is advisable, while Prophet is advisable for longterm forecasting. The study provides valuable recommendations to investors and researchers seeking effective cryptocurrency prediction software.
Abstract This study uses high-frequency price data to analyze risk connectivity among 15 cryptocurrencies, focusing on moments such as volatility, skewness, kurtosis, and jumps during the pre-COVID-19 era, the COVID-19 epidemic, and Russian-Ukrainian tensions. The results indicate that Ethereum Classic is a major shock transmitter in all periods, and this effect becomes more pronounced during geopolitical crises. In contrast, Stellar, Tezos, and Tron are important shock absorbers, particularly during market volatility. Jump risk analysis confirms the dominance of Ethereum Classic and its capacity to increase spillover risks during crises. For higher-order moments, the findings reveal that Bitcoin, Ethereum, and Dash are significant transmitters of skewness spreads, whereas Dash and Eos are significant transmitters of kurtosis spreads. Jump risk analysis confirms the dominance of Ethereum Classic and its capacity to increase spillover risks during crises. These findings highlight the need for targeted risk management strategies adjusted to cryptocurrency market dynamics.
This study aims to analyze the volatility dynamics and spillover phenomena among major crypto assets (Bitcoin, Solana, and Ethereum) and their relationship with the Jakarta Composite Index (JCI), a proxy for the Indonesian capital market. In the era of digital financial integration, the link between speculative crypto asset markets and conventional stock markets is a crucial issue for financial system stability. This study uses daily price time series data for the period 2020-2025. The analysis was conducted using the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and the Diebold-Yilmaz spillover index approach to measure the magnitude of shock transmission between markets. The results indicate significant volatility transmission among the three crypto assets, with Bitcoin remaining the primary source of volatility. Furthermore, this study finds an increasing dynamic correlation between the global crypto market and the Indonesian capital market during periods of economic uncertainty. These findings have important implications for investors in portfolio diversification strategies and for Indonesian regulators in monitoring systemic risks originating from digital assets.
The distributional specification in Markov-switching GARCH models has historically been driven by empirical convention rather than statistical theory. This paper derives the two-regime MS-GARCH specification from the Maximum Entropy Principle, providing an information-theoretic motivation for Student-t regime-conditional innovations in cryptocurrency volatility modelling. The framework is applied to five major cryptocurrencies, Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash, over the period January 2017 to March 2026, comprising 15,834 daily observations spanning six complete market cycles. Three principal findings emerge. First, a Calm-Phase Fragility pattern is identified: four of five assets exhibit calm-regime half-lives below one trading day (0.48 to 1.16 days), with turbulence the dominant long-run state (stationary turbulent probability in [0.451, 0.771] across all assets), establishing turbulence rather than calm as the structural baseline of the cryptocurrency ecosystem. Second, the Maximum Entropy derivation yields endogenous Student-t degrees of freedom, with heavy-tailed turbulent innovations (degrees of freedom approximately 4.5) confirmed across all assets, validating the MaxEnt constraint framework empirically. Third, near-unity turbulent GARCH persistence drives MS-GARCH point forecasts toward the persistence ceiling, consistent with an information-theoretic bound on predictability when the calm half-life collapses below one trading day; HAR-RV achieves the lowest QLIKE loss for three of five assets under these near-critical conditions. Cross-asset consistency is confirmed across seven statistical indicators including Hill tail exponents in [2.31, 3.26], Hurst exponents in [0.543, 0.577], and Wald tests rejecting parameter homogeneity at p < 0.001 for all assets. The framework is formalised as a deployable expert system for real-time regime monitoring and risk management.