This study investigates the relationship between two of the most important assets in the modern market, Bitcoin and gold. While gold has historically been considered a safe-haven asset, Bitcoin has emerged as a new digital alternative to gold. Using daily data from 2014 to 2025, the study applies a purely quantitative comprehensive mathematical framework that includes risk and return analysis, correlation analysis, regression models, granger causality tests, cointegration analysis, vector autoregression and impulse response functions. The results indicate that Bitcoin is a poor alternative to gold for central banks and hedgers, and a successful substitute for gold for speculators and investors, providing higher returns at a higher risk. Furthermore, even though correlation is low, investors may achieve substantial return by focusing on short term market shocks. One of the important results also include that a significant change in Bitcoin price may influence the price of Gold, but changes in the latter do not impact the former. In conclusion, the study recommends the use of Bitcoin and Gold as complements, not as substitutes.
This paper tests whether Bitcoin’s four-year cycle persists in monthlyreturn dynamics after the asset’s recent institutionalization. Weestimate harmonic Fourier regressions with 48- and 24-month componentsand allow the cycle coefficients to shift after a May 2023 structuralbreakpoint. We compare an unconditional model with a macro-conditionedspecification that includes S\&P 500 and U.S. Dollar Index returns.The unconditional results indicate a significant post-break changeand a sharp reduction in cyclical amplitude. However, after controllingfor broader market and liquidity conditions, the residual four-yearcomponent loses statistical significance. The evidence suggests thatBitcoin’s historical halving-related rhythm has weakened and thatits return dynamics are increasingly linked to global macro-financialconditions.
This study examines whether the impact of Tariff Policy Uncertainty (TPU) on gold returns varies depending on Bitcoin market conditions, with the aim of determining whether gold’s safe-haven role is regime-dependent. Using a vector autoregression (VAR) model, Granger causality tests, and impulse response functions (IRFs), the empirical results show that, over the full sample period, TPU has a significantly positive effect on gold returns after a certain lag, confirming that gold partially functions as a safe-haven asset. However, during periods of high Bitcoin investor attention, both the impact of TPU on gold and the causal relationship become statistically insignificant, indicating a weakening of gold’s safe-haven role. In contrast, during low-attention Bitcoin regimes, TPU exerts a strong positive effect on gold returns, accompanied by significant causality and a persistent positive response. These findings suggest that the effects of policy uncertainty shocks on financial markets depend on the substitutive relationship between Bitcoin and gold, implying that gold’s role is partially replaced when Bitcoin attracts high investor attention, while its traditional safe-haven function is reinforced during periods of low attention.
This thesis examines whether cryptocurrencies can function as diversification or risk-reducing assets relative to the Swedish equity market during periods of financial stress. Using daily data for Bitcoin, Ethereum and Ripple from 2018 to 2024, their dynamic relationship with the OMX30 index is analyzed. To provide a broader benchmark, gold, the German DAX index, and the U.S. S&P 500 index are included as comparison assets. Periods of financial stress are identified as episodes in which the OMX30 declines by at least 10 percent from a recent peak. Time-varying correlations are estimated using a Dynamic Conditional Correlation GARCH (DCC-GARCH) model, allowing the analysis of how interasset relationships evolve over time. In addition, hedge effectiveness measures are employed to assess the cryptocurrencies practical ability to reduce portfolio risk.The results show that Bitcoin, Ethereum and Ripple exhibit weak but positive correlations with the Swedish equity market, implying that they may serve as diversifiers but not ashedges or safe-havens. During periods of financial stress, correlations tend to increase rather than decrease, indicating limited protective properties. Hedge effectiveness estimates further suggest that the risk-reducing capacity of cryptocurrencies is unstable and generally weak. Incontrast, gold displays more consistent negative correlations and superior hedging performance. Overall, the findings suggest that cryptocurrencies offer limited diversification benefits for Swedish investors and should not be considered reliable risk-mitigating assets during market stress.
This study investigates time-frequency volatility transmission of both cross-exchange instrument networks and cross-instrument exchange networks of crypto-markets under a unified time-varying parameter vector autoregression (TVP-VAR) framework. 5-minute closing prices of 16 variables throughout the 2021-2025 period are sampled to form the two types of networks by instrument and by exchange, comprising spot and perpetual instruments of Bitcoin (BTC) and Ethereum (ETH) on Binance, OKX, Bitget, and Bitfinex. The hourly logarithmic realized volatility is aggregated to estimate both the time- and frequency-domain connectedness partitioned into short- (1-8 hours), mid- (8-24 hours), and long-term (beyond 24 hours) components. The results indicate that the total connectedness of instrument networks uniformly exceeds that of exchange networks. The long-term component prevails, while the short-term component remains non-negligible with episodic amplification. Bitfinex functions as the sole net receiver across instrument networks, whereas Binance, OKX, and Bitget act as net transmitters. Within exchange networks, ETH instruments more frequently transmit volatility to BTC ones beyond eight hours, while this direction reverses within the 8-hour horizon. Spot instruments dominate perpetuals on OKX, Bitget, and Bitfinex with Binance as the main exception. Eight historical events elicit heterogeneous response modes contingent on the nature of the shocks, with the LUNA collapse and FTX crisis as the most influential in-sample events. The findings carry implications for cross-venue risk monitoring and horizon-aware portfolio management.
This paper studies volatility prediction for Ethereum in the post-Merge era. Using daily ETH/USD returns from 15 September 2022 to 23 April 2026, we compare standard GARCH(1,1), Heston-Nandi GARCH(1,1), cross-validated and aggregated EWMA predictors, and Nadaraya-Watson kernelregression predictors. The kernel forecasts are constructed from a rank-transformed state vector that captures recent volatility and signed-return conditions, allowing the conditional variance function to be nonlinear and state dependent. The results show that forecast performance is strongly horizon dependent. At the one-day horizon, the kernel predictor using the fitted GARCH volatility state delivers the lowest final cumulative squared prediction error, outperforming the standard GARCH benchmark and all EWMA-type competitors. At the ten-day-ahead horizon, the advantage of local nonparametric information weakens, and the mean-reverting structure of GARCH becomes more valuable. The estimated kernel surface reveals that predicted ETH volatility is highest when elevated recent volatility coincides with negative signed-return pressure. Conditional quantile results further show that kernel-based VaR improves lower-tail risk forecasts, especially at the 1% quantile. Overall, the evidence suggests that post-Merge Ethereum volatility is persistent, asymmetric, heavytailed, and nonlinear, and is best modelled by combining economically meaningful volatility states with flexible nonparametric forecasting maps.
We use novel intraday data to study the price discovery process in cryptocurrency markets around U.S. monetary policy, inflation, and labor market announcements. Our analysis reveals the following: (1) volatility, trading volume, and bid-ask spreads rise sharply at announcement times and remain elevated for up to 30 minutes relative to comparable non-announcement intervals, indicating that cryptocurrency investors pay attention to these announcements and that information is quickly incorporated; (2) announcement surprises associated with higher yields or "risk-off" conditions cause substantial cryptocurrency price declines - pointing to a potential strengthening of U.S. monetary policy transmission to the real economy in recent years; (3) the time-varying magnitude and direction of price reactions more closely resemble those of U.S. equities than those of fiat currencies or commodities, suggesting that cryptocurrencies behave primarily as risk-sensitive assets; (4) price impact estimates of order flow around announcements are consistent with rising institutional participation in cryptocurrency markets and their crucial role for price discovery.
Rachid Bourday, Ali Zaaouat, Issam Aattouchi, M. Ait Kerroum
Predicting cryptocurrency prices with precision is crucial for strategic financial planning, enabling stakeholders to mitigate risks in the highly unpredictable nature of digital assets. This paper presents an innovative framework combining Bidirectional Long Short-Term Memory (Bi-LSTM) and Graph Attention Networks (GATs) to improve forecasting accuracy for Ethereum. The Bi-LSTM analyzes time-based trends in historical price and trading volume over a 90-day horizon, whereas GATs examine correlations between critical market features, including 20-day and 30-day moving averages, through attention-focused techniques. When applied to Ethereum's historical price data, the model achieves an MSE of 0.0021, RMSE of 0.046, and MAE of 0.032, exceeding traditional LSTM-based approaches. These outcomes highlight the advantages of fusing sequential neural architectures with graph-structured relational modeling to refine predictive accuracy. By unifying time-series and graph-structured data analysis, this study contributes to the advancement of financial analytics powered by deep learning, equipping traders and researchers with an actionable tool to refine trading tactics within Ethereum's dynamic ecosystem.
We examine whether the institutionalization of digital assets through regulated exchange-traded funds changes the transmission of macro-financial risk. Using daily data from January 2019 to March 2026, we study the launch of the spot Ethereum exchange-traded fund on 23 July 2024 as a dated institutional event and test whether Ethereum’s response to United States inflation surprises changed after the introduction of regulated ETF access. A triple-difference design shows that the interaction between headline Consumer Price Index surprises and lagged Ethereum network activity reverses sign around the ETF launch. Before the ETF, the interaction is small and positive (+0.06, p = 0.04), indicating that a more active network amplified Ethereum’s directional response to inflation news. After the ETF, the interaction becomes large and negative (-0.25, p
Flexible demand is increasingly important in energy systems with high renewable penetration. Bitcoin mining is often cited as a large, theoretically flexible load. Despite electricity consumption rivaling medium-sized industrial economies, the energy market behavior and impacts of Bitcoin miners remain largely unexplored. We exploit the large-scale relocation of Bitcoin mining to Texas, which became the world's largest mining hub following China's 2021 ban, to estimate its effects on local wholesale electricity prices. Combining a novel, hand-collected dataset on mining facility locations with high-frequency wholesale price data, we identify price impacts using a DiD design. We find that miners select into renewable-rich, high-GDP per capita counties with initially lower electricity prices on average. Mining entry has no significant effect on daytime prices but increases nighttime prices by 19.9%, indicating that Bitcoin miners fail to exploit their operational flexibility. Instead they increase baseload demand and reinforce fossil generation during low-renewable periods.
The rapid expansion of sustainable finance and digital assets has created a new frontier where environmental performance and financial systemic risk intersect. This study explores the dynamic spillover structure between sustainable financial instruments (green bonds and green equity indices) and cryptocurrencies classified according to environmental efficiency into ”green” (Proof-of-Stake) and ”conventional” (Proof-of-Work) digital assets. Employing a Time-Varying Parameter Vector Autoregression (TVP-VAR) connectedness framework with daily data from 2022–2024, we quantify evolving return spillovers and systemic interdependencies. Results indicate a pronounced surge in total connectedness in early 2023, followed by stabilization into a new equilibrium regime. Green cryptocurrencies display stronger integration with sustainable financial instruments, while conventional cryptocurrencies function as primary systemic shock transmitters during stress episodes. These findings demonstrate that environmental efficiency has become a financially material characteristic shaping digital asset behavior, linking blockchain technological design to ESG-oriented financial dynamics.
Although many academic studies have examined volatility spillovers and dynamic correlations between stock markets, they have largely overlooked the perspective of Small and Medium-Sized Enterprise (SME) markets. On this basis, this study explores the interconnectedness and volatility correlation between Decentralized Finance (DeFi) markets and SME markets. To understand the correlation between these markets, we empirically analyse six European SME market indices—the FTSE AIM All-Share Index (AIM), BIST SME Industrial Index (BISTSME), Euronext Growth All-Share Index (EURONEXT), First North All-Share Index (FIRSTNORTH), IBEX Medium Cap Index (IBEXC), and Scale All-Share Performance Index (SCALE)—alongside three cryptocurrencies: Aave (AAVE), Ethereum (ETH), and Uniswap (UNI); two stablecoins: Dai (DAI) and USD Coin (USDC); and one synthetic asset: Synthetix (SNX). The study employed BEKK-GARCH and DCC-GARCH to analyse the existence of spillover effects and correlations from October 5, 2020, to August 18, 2024. The findings indicate that AAVE, ETH, and UNI, in particular, transmit significant volatility to the EURONEXT and FIRSTNORTH markets. However, bidirectional volatility spillover was detected between EURONEXT and AAVE, ETH, UNI, USDC, and SNX, and FIRSTNORTH and AAVE, ETH, UNI, and SNX. This suggests volatility interdependence between these markets and the existence of potential risk contagion channels.
This research explores the relationship between abnormal investor attention and Bitcoin futures return by using several Google search keywords covering Bitcoin futures to measure investor attention in its futures market. The empirical findings show that abnormal investor attention significantly negatively correlates to Bitcoin futures return when the market declines. We further consider the effect of COVID-19 and Bitcoin market crash on such a correlation and present that the relation becomes more pronounced during the latter downward periods, but find only a weak effect on such a relation during the epidemic. Finally, we provide evidence after controlling for Bitcoin spot return and VIX that the negative relation between investor attention and Bitcoin futures return is still significant, especially during a Bitcoin crash.
Purpose We investigate the presence of contagion between Bitcoin and four traditional assets (stocks, bonds, gold and the US dollar exchange rate) over the period 2015–2024. Design/methodology/approach We implement a framework that combines the DCC-GARCH specification and a time-varying causal inference methodology. Findings Our findings support that Bitcoin remains weakly connected to the global financial markets. Contagion is limited, appearing sporadically from S&P 500 to Bitcoin and from Bitcoin to the US dollar index. However, when we impose a stricter definition of extreme correlation or a multivariate VAR specification, the contagion results vanish, indicating no systematic contagion between Bitcoin and traditional assets. Practical implications Our evidence implies that Bitcoin may be used as a useful portfolio diversification instrument. Originality/value We deploy a recently developed novel methodology that combines the DCC-GARCH model and a recent time-varying Granger causality procedure to distinguish between extreme high correlation and contagion and find no evidence of systematic contagion effects of Bitcoin with conventional asset classes.
This study investigates the relationship between dirty and clean cryptocurrencies and traditional stock index returns using the Quantile-Quantile (QQR) and Quantile-Quantile Granger Causality (QQGC) methods. The analyses were conducted using daily data from January 2018 to May 2025. QQR results show both positive and negative relationships between dirty and clean cryptocurrencies and the returns of the S&P 500, FTSE 100, TSX, and ASX indices at the low, medium, and high quantiles. According to the QQGC results, both dirty and clean cryptocurrencies showed predictive power for the returns of the S&P 500, FTSE 100, TSX, and ASX indices at different quantiles. Furthermore, it was found that both dirty and clean cryptocurrencies exhibit strong predictive power for S&P 500 and FTSE 100 returns, particularly in the middle quantiles. The results obtained reveal that distinguishing between dirty and clean cryptocurrencies under different market conditions provides important insights for investors' portfolio diversification strategies and risk management practices.
The rapid expansion of cryptocurrencies and decentralized finance (DeFi) has redefined global financial systems, creating new challenges in asset pricing, risk measurement, and systemic stability. This study conducts a comprehensive review of 93 peer-reviewed articles published between 2019 and 2024 to consolidate the fragmented literature on mathematical models applied to cryptocurrencies and DeFi platforms. Using a mixed bibliometric–systematic approach based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework, the review integrates performance indicators, conceptual mapping, and qualitative synthesis to identify methodological advances and research trends. The findings reveal a progressive convergence between econometric models, such as the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), stochastic volatility, and Lévy processes, and data-driven approaches based on machine learning (ML), deep learning (DL), and reinforcement learning (RL). These hybrid frameworks enhance predictive accuracy and adaptability in high-frequency and non-linear blockchain markets. The review also highlights optimization-based decision models that integrate Conditional Value-at-Risk (CVaR), network theory, and portfolio analytics for decentralized finance operations. However, interpretability, governance, and environmental sustainability remain underexplored dimensions. The study contributes by classifying mathematical approaches to pricing, volatility, and risk propagation, identifying methodological gaps, and recommending future research on explainable artificial intelligence (AI), environmental and cyber-risk modeling, and real-time validation for transparent and resilient decentralized financial ecosystems. • Review 93 studies analyzing mathematical models in cryptocurrency and digital finance systems. • Identify emerging methods for pricing, risk, and portfolio decisions under high volatility. • Compare deep learning models to traditional methods for forecasting and risk evaluation. • Evaluate decision models that include environmental, risk, and governance factors. • Recommend future research on interpretable tools for real-time decision-making.
This research investigates the predictive power of news sentiment from Google News on Bitcoin price movements, leveraging a five-year dataset of news headlines (2019 to 2024). By correlating sentiment scores with historical Bitcoin prices, the study employs various machine learning algorithms to forecast price trends. The results indicate that while Decision Tree and Random Forest models offer balanced predictions, Logistic Regression and Support Vector Machines achieve high AUC scores but suffer from class imbalance. In contrast, Naïve Bayes and KNN models prove less effective. The findings suggest that sentiment analysis of news headlines can provide moderate short-term predictions for Bitcoin price fluctuations. This study introduces an innovative tool for investors and market analysts, offering insights into the influence of news sentiment on cryptocurrency prices.
This paper investigates the Granger causality relationship in Bitcoin mining from environmental, sustainable, and miner’s financial perspectives for the period of February 2017 to January 2025. Using a time-varying Granger causality approach of Shi et al. (2018,2020), we explore how the hashrate, a measure of computational power in the Bitcoin mining process, affects energy consumption, electronic waste, and miners’ revenues. Our findings reveal that an increase in hashrate leads to a significant rise in energy use and e-waste and affects miners’ revenues. In addition, we show that mining revenue Granger causes the hashrate, suggesting economic incentives drive the network security through the hashrate. These results offer new insights for investors, policymakers, and environmental economists. • A time-varying Granger causality approach is adopted. • Higher computational power directly increases electricity demand and electronic waste. • The intensity of competition, as measured by hashrate, has a significant impact on mining profitability. • Higher mining revenues incentivise the use of greater hash power.
ABSTRACT Based on the rationale that returns and volatility are interrelated, we apply a multilayer network framework involving the return layer and volatility layer of cryptocurrencies, NFTs, and DeFi assets over the period January 1, 2018–January 23, 2024. The results show significant connectedness in each of the return and volatility layers, with major cryptocurrencies such as Bitcoin and Ethereum playing a central role. Large spikes in the level of connectedness are noticed around COVID‐19 pandemic and Russia–Ukraine conflict, and Bitcoin and Ethereum emerge as net transmitters of returns and volatility shocks, emphasizing their significant role around these crisis periods. Notably, a strong positive rank correlation exists between the return and volatility layers, highlighting the significant risk–return relationship in the digital asset class. The findings suggest that economic actors should not ignore the interconnectedness between the return and volatility layers in the system of cryptocurrencies, NFTs, and DeFi assets for the sake of a comprehensive analysis of information flow. Otherwise, a share of the information flow concerning the return–volatility nexus across these digital assets would be missed, possibly leading to inferences regarding asset pricing, portfolio allocation, and risk management.
M. S. F. Nasrifa, R. P. D. M. Amarasinghe, W. M. P. K. Weerasinghe
The purpose of this research is to explore how investor attention, measured by GSVI, influences cryptocurrency market behavior under varying conditions. For this the study examines the impact of Google Search Volume Index (GSVI) on cryptocurrency returns, considering market uncertainty, news sentiment, and the COVID-19 pandemic. A regression analysis was conducted using datasets covering BNB, Bitcoin, Dogecoin, Solana, and Tether from 2015 to 2022. Stata was used to estimate the relationships between cryptocurrency returns and key variables, ensuring accurate and reliable results to quantify the relationships. Our findings indicate that abnormal increases in GSVI positively affect cryptocurrency returns, particularly during high uncertainty periods and when news sentiment is favorable. Moreover, the effect of investor attention on returns was significantly amplified during the COVID-19 pandemic, suggesting that global crises has heightened the role of behavioral factors in cryptocurrency markets. This research contributes to the literature by integrating investor attention with uncertainty and sentiment measures, offering a comprehensive view of cryptocurrency price dynamics. Unlike previous studies that examine these factors in isolation, our study highlights their combined effect, providing valuable insights for investors, policymakers, and analysts in understanding market trends and decision-making strategies.
The bitcoin market has exhibited highly volatile return movements, experiencing a sharp surge starting from in November 2022 to 2024. This significant fluctuation underscores the importance of analyzing the factors influencing bitcoin’s return dynamics. This study utilizes daily data with a final sample of 590 observations. All time-series variables must be stationary before being processed in the statistical model. The analysis was conducted using Stata 16 software. To ensure the absence of unit roots, the stationarity of the research variables was tested using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests. The findings indicate that market capitalization, gold, and litecoin have no significant impact on bitcoin returns. In contrast, miners’ revenue has a significant negative effect, while hashrate, mining difficulty, and the S&P 500 exhibit a significant positive influence on bitcoin returns. This study highlights bitcoin’s role as a store of value and investment asset, emphasizing the impact of hashrate and mining difficulty on its returns and integration into financial markets, particularly the S&P 500. The findings provide insights for investors on portfolio diversification and assets like a gold and equities. Additionally, the study underscores the importance of sustainable mining practices and regulatory policies to balance cryptocurrency’s economic potential with environmental sustainability. Keywords: Market capitalization; Mines’s Revenue; Hashrate; Mining difficulty; Commodity Asset, Cryptocurrency