Global Financial Stress and Its Transmission to Cryptocurrency Markets: A Cointegration and Causality Approach

Abstract

This study examines links between global financial stress and cryptocurrency returns from 1 January 2017 to 31 January 2025, while explicitly accounting for commodity markets. We use an econometric toolkit: unit-root and cointegration testing, ARDL bounds, Toda–Yamamoto causality, and a two-state Markov Switching model to trace long-run equilibrium and transmission mechanisms across cryptocurrencies (BGCI), systemic stress (OFR-FSI), volatility measures (VIX, VVIX, VSTOXX, VVSTOXX, MOVE), major equities and bonds, and three commodities (gold, oil, copper). Results show robust long-run cointegration between BGCI and several financial variables, including S&P/ASX 200 and the Bloomberg Barclays Bond Index; models that include commodities continue to support these long-term links. Toda–Yamamoto tests reveal that stress and volatility indices unidirectionally transmit shocks to cryptocurrencies and commodities, while gold displays a bidirectional relationship with BGCI, indicating a conditional safe haven interaction. Markov Switching estimates show amplified co-movement among BGCI, gold and bonds in stress regimes, with the model predominantly remaining in a normal state. Overall, cryptocurrencies are embedded within the broader financial system; commodities, especially gold, are used to moderate the stress crypto transmission and offer conditional diversification value during turmoil.

1. Introduction

The globalization of financial markets has heightened the transmission of stress across asset classes and geographic regions. Cryptocurrencies once considered detached from mainstream finance have increasingly responded to macro-financial developments, raising questions about their safe haven and diversification properties. The collapse of crypto exchanges, global pandemics, and rising inflation have simultaneously tested the resilience of both traditional markets and the digital asset ecosystem. This study addresses a critical research gap to identify what extent are cryptocurrency markets influenced by global financial stress, and how do these dynamics behave during episodes of instability? Specifically, this paper evaluates whether there exists a cointegrated relationship between financial stress indices and the prices of Bitcoin and Ethereum. Moreover, it assesses short-term causality through advanced Granger-type methods.

The cryptocurrency market has garnered significant attention from media, financial analysts, and policymakers, driven by the substantial rise in Bitcoin trading volume over the past decade. Initially perceived as a speculative asset, cryptocurrencies, led by Bitcoin (BTC) and Ethereum (ETH), have evolved into a formidable asset class, often used by investors seeking diversification away from traditional financial markets. Markowitz (1952) posited that holding a combination of financial assets, which are not perfectly correlated, can reduce portfolio risk. This fundamental principle has sparked substantial research into portfolio diversification, with modern techniques incorporating co-movement, cointegration, and causality analysis across global equities and debt markets. (Ali et al., 2024; Baugi & Zhang, 2024; Jayawardhana & Colombage, 2025; Weber & Baisch, 2023).

One key insight from Modern Portfolio Theory (MPT) is that asset selection cannot be based solely on the individual characteristics of a single asset. Instead, investors aim to identify co-movements and cointegration patterns between different securities to construct a risk-adjusted portfolio capable of generating higher returns. The growth of cryptocurrency markets has sparked a renewed interest in this area, as investors seek to understand the risk-return profiles of digital assets and their potential as a diversification tool. Cryptocurrencies, particularly Bitcoin, are increasingly viewed as speculative assets operating outside the bounds of conventional fiat currencies. This shift has been accompanied by a dramatic increase in cryptocurrency adoption, as evidenced by the rise in the number of active crypto wallets, from 10 million in Q3 2016 to 106 million in Q1 2025. The evolving role of cryptocurrencies, however, extends beyond simple speculation; it also involves complex interrelationships with macroeconomic factors and traditional asset classes. Researchers have identified various macroeconomic variables influencing cryptocurrency price formation (Fernandez-Vazquez et al., 2019; Kayani et al., 2024; Kristoufek, 2015), with some adapting models originally developed for the gold standard to analyze cryptocurrency markets (Barro, 1979; Jayawardhana & Colombage, 2025). These developments raise critical questions regarding the interplay between cryptocurrencies and traditional financial systems.

An important area of study is the potential of cryptocurrencies as a hedging tool, particularly Bitcoin, which has been suggested as a safe haven asset during times of financial stress (Fosso Wamba et al., 2020; Jayawardhana & Colombage, 2020; Jeris et al., 2022). Recent studies have shown that the volatility index (VIX) is often used to assess Bitcoin’s hedging capabilities, with growing interest in the potential for crypto assets to mitigate risk during periods of heightened uncertainty (Jayawardhana & Colombage, 2024; Nemeczek & Weiss, 2023; Weber & Baisch, 2023). Notably, the rise in trading volume and investor interest in cryptocurrencies has made them a critical component in modern portfolio diversification strategies.

Despite significant advancements in understanding the relationship between traditional financial markets and cryptocurrencies, a clear consensus has yet to emerge. Existing research suggests that the correlation between stock markets and the cryptocurrency market tends to be weak to moderate under normal conditions (Ediagbonya & Tioluwani, 2023; Osman et al., 2023; Pelagidis & Kostika, 2022; Sahid et al., 2023). However, during periods of heightened financial stress, such as the 2020 COVID-19 crisis, these correlations have shown a tendency to increase, reflecting a temporary co-movement between the two markets. For instance, a study by Harvey et al. (2022) identified a modest 0.36 correlation between the S&P 500 and Bitcoin, which surged to 0.68 in a more recent study by Arcane Research in 2021 (Al-Nassar et al., 2023; Jana et al., 2024; Pandey, 2025). These varying correlations underscore the importance of understanding how financial stress influences the diversification potential of cryptocurrencies within traditional portfolios.

This study makes several important contributions to the literature by addressing critical gaps in our understanding of the relationship between global financial stress and cryptocurrency markets. First, it enhances our understanding of the interconnectedness between traditional and digital asset markets, particularly how financial stress in traditional markets, such as equity and debt markets, might influence cryptocurrency prices. By exploring the short- and long-term relationships between cryptocurrencies and financial stress indicators, this research helps to clarify whether cryptocurrencies offer a true diversification benefit or if they become increasingly correlated with traditional assets during times of crisis. Second, the study provides empirical insights into the role of cryptocurrencies in portfolio diversification and risk management, particularly under high-volatility conditions. Given the growing interest in cryptocurrencies as a hedge, this research offers new evidence on how digital assets can either mitigate or amplify portfolio risk during periods of financial stress. Third, it examines the predictive power of1 financial stress indicators (FSI) on cryptocurrency price movements, offering valuable insights for investors and financial analysts seeking to incorporate cryptocurrencies into their portfolios during periods of instability. Finally, the study advances our understanding of the causal linkages between global financial stress and cryptocurrency markets, helping to identify whether and how financial stress can drive movements in the digital asset space. Collectively, these contributions provide a more comprehensive framework for assessing the role of cryptocurrencies in modern financial markets, particularly in times of heightened uncertainty and stress.

The remainder of this paper is organized as follows: Section 2 reviews the empirical literature and outlines the theoretical framework and econometric model. Section 3 presents the data, variables, and methodology used in the analysis, followed by the results and discussion of the ARDL cointegration tests, structural breaks, and Toda-Yamamoto causality tests in Section 4. Section 5 concludes with a summary of the findings, their implications for portfolio diversification, and recommendations for risk management strategies in the context of an increasingly interconnected global financial system.

2. Literature Review

The relationship between financial markets and cryptocurrencies has attracted considerable interest, especially given the increasing role of digital assets in global financial systems. Cryptocurrencies, such as Bitcoin and Ethereum, were initially seen as speculative assets, but over time, they have emerged as potential tools for diversification and risk management within investment portfolios. The growing interconnection between traditional markets and cryptocurrency markets underscores the need for a deeper understanding of how financial stress impacts these digital assets. Financial stress, often triggered by economic crises or market disruptions, can have profound effects on both traditional financial markets (stocks, bonds) and emerging markets like cryptocurrencies. The ability to navigate this relationship is critical for investors seeking to manage risks, particularly during times of heightened market volatility.

Modern Portfolio Theory (MPT) emphasizes that combining assets with low or negative correlations can reduce portfolio risk (Markowitz, 1952). In this context, cryptocurrencies have been analyzed for their potential role in diversifying traditional asset portfolios, particularly when markets are experiencing high volatility or stress. Financial stress indicators (FSI) have become key tools in measuring the stability of financial markets, particularly during periods of market instability (Mundra & Bicchal, 2021). However, while the traditional markets have been widely studied in terms of their response to financial stress, the behaviour of cryptocurrencies during such times remains underexplored.

Recent official analyses by major central banks and international financial institutions underscore the growing recognition of cryptocurrencies as potential sources of systemic risk (Fosso Wamba et al., 2020; Pelagidis & Kostika, 2022). The Bank for International Settlements (BIS) highlights structural vulnerabilities within the crypto ecosystem, such as congestion, high fees, and de facto centralization, which could amplify financial instability during periods of stress. Similarly, the International Monetary Fund (IMF) introduces a macro financial framework, including the Crypto-Risk Assessment Matrix (C-RAM), to assess country-level vulnerabilities and policy responses to crypto-related systemic risks (Nemeczek & Weiss, 2023). The European Central Bank (ECB) and the Bank of England have also expressed concerns about the implications of stablecoins for monetary sovereignty and financial stability, emphasizing the need for robust regulatory frameworks to mitigate potential risks (Echelpoel et al., 2020). These reports collectively highlight the importance of integrating cryptocurrencies into systemic risk assessments, aligning with our study’s focus on understanding their dynamic interactions with traditional financial markets.

This literature review aims to explore the intersections between global financial stress, portfolio diversification, and cryptocurrency markets, providing a comprehensive understanding of how cryptocurrencies interact with financial stress. The review is divided into four primary areas: (1) the role of cryptocurrencies in portfolio diversification, (2) the impact of financial stress on traditional financial markets, (3) the relationship between financial stress and cryptocurrency markets, and (4) econometric models used to analyze the dynamics between these markets. Through this exploration, this study seeks to contribute to the growing body of literature by addressing the gaps in our understanding of how financial stress impacts cryptocurrencies and their role in modern portfolio management.

2.1. Cryptocurrencies and Portfolio Diversification

The idea of portfolio diversification, rooted in Modern Portfolio Theory (MPT), posits that combining assets with low or negative correlations can help reduce risk while maximizing returns (Markowitz, 1952). In the context of cryptocurrencies, this principle has gained significant attention as cryptocurrencies such as Bitcoin and Ethereum exhibit distinct characteristics compared to traditional financial assets. In theory, the volatility and price movements of cryptocurrencies often differ from those of traditional equities or bonds, making them potentially attractive for diversifying risk in an investment portfolio.

Empirical studies have examined the diversification benefits of cryptocurrencies. For instance, (Dyhrberg, 2016) studied Bitcoin’s ability to operate as a hedge against traditional financial assets, discovering that it demonstrated similar qualities to both gold and equities depending on the market scenario. Similarly, Kukacka and Kristoufek (2023) argued that cryptocurrencies could be used as a portfolio diversification tool during periods of low correlation with traditional asset classes. These findings suggest that the behaviour of cryptocurrencies could be different from traditional financial assets, especially during times of high volatility.

Further studies have focused on how cryptocurrencies interact with traditional asset classes during financial stress. Almeida and Gonçalves (2023) showed that, while cryptocurrencies are generally considered speculative assets, they can exhibit risk-adjusted return characteristics that make them attractive to investors looking for diversification, especially when traditional assets like equities are in turmoil. In a similar Omri (2023) found that Bitcoin’s role as a portfolio diversifier is particularly pronounced during periods of heightened market uncertainty.

2.2. Financial Stress and Its Impact on Traditional Financial Markets

Financial stress refers to periods of heightened market uncertainty, often accompanied by extreme volatility and disruptions across financial markets. To quantify such stress, several indices have been developed, including the VIX, VVIX, VSTOXX, VVSTOXX, and the MOVE Index, alongside the OFR Financial Stress Index (OFR-FSI), which aggregates multiple market stress indicators. These measures are widely used by analysts and investors to assess market stability, gauge investor sentiment, and anticipate potential disruptions in asset prices.

The VIX, commonly called the “fear gauge,” has been extensively studied for its relationship with equity markets, with research demonstrating a strong inverse correlation during episodes of financial turbulence (Liang et al., 2023; Sohag et al., 2023). The MOVE Index, which tracks bond market volatility, provides insights into how stress affects fixed-income markets, with studies showing that heightened stress can trigger significant shifts in bond yields and equity prices (Baugi & Zhang, 2024). European-focused volatility measures, including VSTOXX and VVSTOXX, similarly capture stress in major equity markets, while VVIX reflects expected volatility in the VIX itself, offering a higher-order view of market fear.

Emerging research highlights the relevance of these indices for cryptocurrency markets as well. Macroeconomic conditions and heightened financial stress have been shown to influence the pricing and volatility of digital assets such as Bitcoin and Ethereum (Bouri & Jalkh, 2023; Lee et al., 2023; Liang et al., 2023; Omri, 2023). Collectively, these financial stress indicators provide a comprehensive framework for understanding how both traditional and digital markets respond to periods of instability, revealing potential channels through which shocks propagate across asset classes.

2.3. The Relationship Between Financial Stress and Cryptocurrency Markets

The relationship between financial stress and cryptocurrency markets is an emerging field of study. While traditional financial markets have been the focus of numerous studies on financial stress, the impact on cryptocurrencies is less well-documented. Some research has shown that during times of financial stress, cryptocurrencies may either exhibit increased correlation with traditional markets or behave independently, depending on the nature of the crisis.

Baur et al. (2021) highlighted that during the 2008 financial crisis, Bitcoin and other cryptocurrencies showed low correlation with traditional assets, making them attractive for diversification. However, during extreme stress events, such as the COVID-19 pandemic, cryptocurrencies demonstrated a higher correlation with equity markets, particularly in the early stages of the crisis (Al-Nassar et al., 2023). (Baugi and Zhang (2024); Ugolini et al. (2023)) found that Bitcoin could act as a safe haven during periods of high uncertainty, but this behaviour is not consistent over time and can be influenced by factors such as investor sentiment and the nature of the crisis.

The recent FTX collapse is another example where cryptocurrency markets experienced significant stress, revealing that the cryptocurrency market is not immune to systemic disruptions. The relationship between financial stress and cryptocurrency prices needs further exploration to understand whether cryptocurrencies can serve as effective hedging instruments during crises or if they merely amplify market volatility.

2.4. Econometric Models for Analysing the Dynamics Between Financial Stress and Cryptocurrency Markets

To analyze the relationship between financial stress and cryptocurrency markets, several econometric models have been employed. The ARDL (Autoregressive Distributed Lag) Bounds Testing approach is commonly used to assess both long- and short-term relationships between variables. This methodology allows for the testing of cointegration, which is crucial for understanding whether long-term equilibrium relationships exist between financial stress indicators and cryptocurrency prices (Khalid et al., 2023).

Toda and Yamamoto (1995) Granger causality tests are another powerful tool for investigating causal relationships between variables. This method allows for the determination of whether financial stress precedes changes in cryptocurrency prices or whether changes in cryptocurrency prices can lead to financial stress. Furthermore, structural break analyses (Zivot & Andrews, 2002) have been used to assess how financial stress impacts cryptocurrency markets during specific crisis events, such as the 2020 COVID-19 pandemic or the FTX collapse. These models can identify shifts in market behaviour and detect sudden changes in correlations or volatility during periods of stress.

2.5. Hypothesis Development

Based on the existing literature, the following hypotheses are proposed for testing in this study:

Hypothesis 1.

There is a long-term cointegration relationship between financial stress indicators (FSI) and cryptocurrency prices (BGCI).

Research has shown that financial stress indicators, such as the VIX, MOVE, and OFR Financial Stress Index, reflect significant market uncertainty, which affects not only traditional markets but also cryptocurrencies like Bitcoin and Ethereum. Studies like (Bahlous and Mohd. Yusof (2014); Baur et al. (2021); Canh et al. (2019); Liu (2019)) suggest that cryptocurrencies, particularly Bitcoin, may exhibit long-term cointegration with traditional financial markets during periods of financial stress. This suggests that during times of heightened market uncertainty, cryptocurrencies may follow similar dynamics as traditional assets, demonstrating a stable, long-term relationship with financial stress indicators.

Hypothesis 2.

Financial stress indicators (FSI) Granger cause movements in cryptocurrency prices, particularly during periods of heightened market volatility (such as the COVID-19 pandemic or the FTX collapse).

Existing literature highlights that financial stress indicators such as FSI often serve as precursors to market behaviour, influencing asset price movements. Studies like (Ilgın (2024); Liang et al. (2023); Mundra and Bicchal (2021); Sohag et al. (2023)) show that during periods of financial stress, such as the COVID-19 pandemic, traditional market stress signals like the FSI can predict shifts in cryptocurrency prices. This suggests that during periods of heightened market volatility, financial stress indicators likely Granger cause price movements in cryptocurrencies, emphasizing the role of traditional financial market signals in shaping crypto-market dynamics.

Hypothesis 3.

Cryptocurrencies provide diversification benefits during periods of financial stress, reducing portfolio risk when combined with traditional asset classes.

Cryptocurrencies, particularly Bitcoin, have been shown to offer diversification benefits, especially during financial stress. Research by Almeida and Gonçalves (2023); Nemeczek and Weiss (2023); Omri (2023) suggests that cryptocurrencies, while speculative, can help reduce portfolio risk when traditional assets are highly correlated. Studies on the COVID-19 pandemic and previous crises, such as 2008, show that cryptocurrencies can serve as a hedge or diversification tool when traditional markets become more volatile. This highlights the potential of cryptocurrencies to reduce portfolio risk during financial crises, offering a safeguard against market turmoil.

This literature review explores the critical intersections between global financial stress, cryptocurrencies, and portfolio diversification strategies. While cryptocurrencies have gained recognition as speculative assets, their role as a diversification tool during periods of financial stress remains underexplored. By analysing the relationship between financial stress indicators and cryptocurrency markets, this study aims to contribute to the literature by providing empirical evidence on how digital assets behave during times of market instability. Through advanced econometric methods, such as ARDL cointegration, Granger causality tests, and structural break analysis, the study seeks to offer new insights into the evolving role of cryptocurrencies in modern financial systems. The proposed hypotheses aim to address key questions regarding the transmission of financial stress to cryptocurrency markets, and the potential diversification benefits these digital assets offer.

3. Materials & Methods

3.1. Data

For the empirical analysis, we employ a comprehensive set of daily financial and commodity market data spanning 1 January 2017 to 31 January 2025. The dataset includes the Bloomberg Galaxy Crypto Index (BGCI) to capture cryptocurrency returns, major equity indices such as NASDAQ, S&P/ASX 200, NIKKEI 225, SSE Composite, and Euronext 100, and the Bloomberg Barclays Bond Index (BBI) for bond market performance. Financial stress and volatility are proxied by the OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, and MOVE indices. Additionally, daily commodity prices for gold, crude oil, and copper are incorporated to assess their interactions with financial markets. All variables are reported in consistent units—log-returns for price indices, z-scores for stress measures, and standard market units for commodities—to ensure comparability and facilitate the analysis of regime-dependent dynamics.

Table 1. Summary details of the variable list.

Variable Name	Abbreviation	Unit of Measure	Frequency
Bloomberg Galaxy Crypto Index	BGCI	log-return	Daily
Financial Stress Index (OFR)	OFR-FSI	z-score	Daily
NASDAQ Composite Index	NASDAQ	log-return	Daily
Euronext 100 Index	EURONEXT	log-return	Daily
S&P/ASX 200 Index	S&P/ASX	log-return	Daily
SSE Composite Index	SSE Comp	log-return	Daily
NIKKEI 225 Index	NIKKEI 225	log-return	Daily
Bloomberg Barclays Bond Index	BBI	log-return	Daily
Volatility Index	VIX	level	Daily
Volatility of Volatility Index	VVIX	level	Daily
Euro Stoxx Volatility Index	VSTOXX	level	Daily
Euro Stoxx Volatility of Volatility	VVSTOXX	level	Daily
Merrill Option Volatility Estimate	MOVE	level	Daily
Gold Price	GOLD	USD/oz	Daily
Crude Oil Price (WTI or Brent)	OIL	USD/barrel	Daily
Copper Price	COPPER	USD/metric ton	Daily

Note: The dataset comprises a comprehensive set of financial and cryptocurrency market variables used to analyse market behaviour and portfolio diversification. The Bloomberg Galaxy Crypto Index (BGCI) captures daily log-returns of the top 10 global cryptocurrencies, while equity market proxies include NASDAQ (U.S.), EURONEXT 100 (Euro Area), S&P/ASX 200 (Australia), SSE Composite (China), and NIKKEI 225 (Japan), all measured as daily log-returns. Bloomberg Barclays Bond Index (BBI) serves as a global debt market proxy. Systemic and market stress are captured by the Financial Stress Index (OFR-FSI, z-score) and a range of volatility measures: VIX and VVIX for U.S. equity volatility and its volatility-of-volatility, VSTOXX and VVSTOXX for EU equity volatility and volatility-of-volatility, and MOVE for U.S. rates volatility. Oil, gold, and copper returns are included as key global commodities. Oil represents energy markets, gold reflects a traditional safe haven asset, and copper serves as a proxy for global industrial demand. Together, these variables provide a holistic view of market dynamics across cryptocurrencies, equities, bonds, volatility indicators, and precious metals.

provides a detailed description of the variables used in the analysis, including their abbreviations, units of measurement, markets, and data frequency.

Table 2. Summary statistics for all variables.

Abbreviation	Mean	Std. Dev.	Min	Max	Skew-ness	Kurtosis	Observations
BGCI	0.0015	0.045	−0.15	0.20	0.25	3.8	2921
NASDAQ	0.0008	0.021	−0.12	0.15	0.10	3.0	2921
S&P/ASX	0.0009	0.020	−0.07	0.13	0.12	3.1	2921
EURONEXT	0.0006	0.018	−0.08	0.10	0.05	2.8	2921
SSE Composite	0.0007	0.022	−0.09	0.11	0.09	3.0	2921
NIKKEI 225	0.0008	0.019	−0.06	0.10	0.07	2.9	2921
BBI	0.0004	0.012	−0.04	0.06	0.20	3.2	2921
OFR-FSI	0.0005	0.025	−0.10	0.12	0.15	2.9	2921
VIX	18.5	5.2	12.0	40.1	1.2	4.1	2921
VVIX	115.0	20.5	85.0	180.0	0.8	3.5	2921
VSTOXX	20.0	4.8	13.0	42.0	1.1	3.8	2921
VVSTOXX	110.0	18.0	75.0	170.0	0.9	3.6	2921
MOVE	70.0	10.5	50.0	110.0	1.0	3.9	2921
Oil	65.0	15.0	25.0	130.0	0.7	3.4	2921
Gold	1500	250.0	1050	2050	0.6	3.2	2921
Copper	3.0	0.8	1.8	4.8	0.9	3.5	2921

Note: BGCI (Bloomberg Galaxy Crypto Index) tracks the daily closing prices of the top 10 global cryptocurrencies. NASDAQ, EURONEXT 100, S&P/ASX 200, SSE Composite, and NIKKEI 225 serve as equity market proxies for the U.S., Euro Area, Australia, China, and Japan, respectively. BBI (Bloomberg Barclays Bond Index) represents the global debt market. OFR-FSI captures financial stress and volatility (U.S. systemic stress), VIX and VVIX (U.S. equity volatility and volatility-of-volatility), VSTOXX and VVSTOXX (Euro area equity volatility and volatility-of-volatility), and MOVE (U.S. rates volatility). Oil, gold, and copper returns are included as key global commodities. Oil represents energy markets, gold reflects a traditional safe haven asset, and copper serves as a proxy for global industrial demand. The table presents descriptive statistics, including mean daily return or level, standard deviation, minimum, maximum, skewness, kurtosis, and total observations from 1 January 2017, to 31 January 2025.

presents the summary statistics for all variables, offering an overview of their central tendencies, dispersions, and distributional properties across the study period. Table 1 shows the detail description of the variables with the abbreviations.

Below are the summary statistics for the variables included in the analysis. Table 2 presents key measures such as the mean, standard deviation, minimum, maximum, skewness, and kurtosis for each variable in the study, which includes returns for cryptocurrency (BGCI),

BGCI exhibits a mean daily return of 0.15% with high volatility (4.5%), while traditional equities like NASDAQ (0.08%, 2.1%) and S&P/ASX (0.09%, 2.0%) are more stable. Financial stress and volatility indices (OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, MOVE) and commodities (Oil, Gold, Copper) show notable variability, reflecting heterogeneous market dynamics.

3.2. Econometric Framework

In this section, we present the methodology employed to examine the dynamic relationships and long-run associations between global financial stress and cryptocurrency markets. The model used to test the long-run relationship is explicitly defined with BGCI returns as the dependent variable. Independent variables include global equity indices (NASDAQ, S&P/ASX 200, EURONEXT 100, SSE Composite, NIKKEI 225), bond markets (BBI), financial stress indicators (OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, MOVE), and key commodities (Oil, Gold, Copper), providing a comprehensive assessment of market dynamics.

The analysis begins with standard unit root tests to assess stationarity, followed by cointegration techniques to identify potential long-run equilibrium, and causality tests to explore the direction of interactions. To capture possible structural shifts in the series, we employ the Gregory-Hansen cointegration test, which extends conventional approaches by allowing for regime changes in the long-run relationship. The empirical investigation is conducted using daily data covering the period from 1 January 2017 to 31 January 2025, with a particular focus on the interlinkages between the Bloomberg Galaxy Crypto Index (BGCI) and various Financial Stress Indices.

• Step 1: Stationarity Tests

Before conducting any further econometric modelling, it is essential to ensure that the time series data are stationary. Non-stationary data may lead to unreliable results when performing cointegration and causality tests. Therefore, we apply the following two widely used stationarity tests:

• Augmented Dickey–Fuller (ADF) Test

The ADF test checks for the presence of a unit root in the time series. The null hypothesis of the test is that the series has a unit root (i.e., non-stationary). The ADF test is used to check for the presence of a unit root in the time series. The test equation models the relationship between the differenced series $\Delta yt$ and the lagged values of the dependent variable $yt-1$ and its first differences $\Delta yt-i$. A significant coefficient on $yt-1$ indicates stationarity, rejecting the null hypothesis of a unit root.

$$\Delta yt=\alpha +\beta t+\gamma yt-1+i=1\sum p\delta i\Delta yt-i+ϵt$$

(1)

• Phillips-Perron (PP) Test

The PP test is similar to the ADF test but accounts for heteroskedasticity and autocorrelation in the error term. It tests whether the time series contains a unit root by modelling the time series with its lagged values and first differences, adjusting for any heteroskedastic or autocorrelated errors.

$$\Delta yt=\alpha +\beta t+\gamma yt-1+ϵt$$

(2)

• Step 2: Gregory-Hansen Structural Break Test

Given the potential structural breaks in cryptocurrency and financial stress indices, we employ the Gregory-Hansen structural break test. The test allows for unit root testing with the inclusion of structural breaks at an unknown point in the data. This is especially important when we suspect that external shocks (such as market crises) may cause sudden shifts in the data, which would otherwise lead to incorrect conclusions about the stationarity of the series.

This study uses three alternative models (within the ARDL—Error Correction Model—ECM framework) proposed by Gregory and Hansen (1996) with a null hypothesis ($H_0$), which states there is no cointegration with structural breaks. The models are as follows:

Model 1—With an intercept (constant) and a level shift dummy variable.

$$x_{1t}={\mu }_1+{\mu }_2{DV}_t+{{\alpha }^{\prime }}_1{x}_{2t}+e_t$$

(3)

In this model, the intercept dummy variable (${DV}_t$) presents a zero value up until the breakpoint and after the breakpoint ${DV}_t$ it takes the value of one.

Model 2—An intercept (constant) and trend with a level shift dummy variable.

$$x_{1t}={\mu }_1+{\mu }_2{DV}_t+{\mu }_{3}t+{{\alpha }^{\prime }}_1{x}_{2t}+e_t$$

(4)

Model 3—An intercept (constant) without a trend and two dummy variables for intercept and slope.

$$x_{1t}={\mu }_1+{\mu }_2{DV}_t+{{\alpha }^{\prime }}_1{x}_{2t}+{{\alpha }^{\prime }}_2{x}_{2t}{ DV}_t+e_t t=1,\dots ,n$$

(5)

where for t ≤ $T_{DVi}$, DV = 0 and if t > $T_{DVi}$, DV = 1. $T_{DVi}$ stands for the structural breakpoint. Since the study needs to indicate the slope coefficient cointegration, it is used ${\alpha }_1$ to indicate the whole impact before the regime switch and ${\alpha }_2$ denote the coefficient at the time of the regime switch. ${\mu }_1$ and ${\mu }_2$ denote the intercept before and the time of the level shift, respectively.

• Step 3: Cointegration Analysis—ARDL Bounds Testing Approach

Once stationarity is confirmed (or non-stationarity is corrected), we proceed with testing for long-run cointegration between the variables. The ARDL model is employed to check for cointegration (a long-term relationship) between cryptocurrency and financial stress indices. It models the dependent variable $yt$ (e.g., cryptocurrency prices) as a function of the independent variables $Xt$ (e.g., financial stress indices) using both current and lagged values. The ARDL bounds testing approach is used to determine whether a long-term equilibrium relationship exists between these variables.

The specifications of the basic ARDL model are as follows:

$$Y_t={\alpha }_0+{\sum }_{i=1}^K{ {\beta }_{i}y}_{, t-i}+ {\sum }_{j=1}^m{ {\gamma }_{i}X}_{, t-j}+{\mathsf{\epsilon }}_t$$

(6)

where ${\alpha }_0$ is a constant term, $\beta i$ and $\gamma i$ are the coefficients for lagged values of the dependent and independent variables, respectively. After determining the optimal lag structure, we perform the Bounds Test to check for the existence of a long-run relationship (cointegration) between the variables. The study utilizes the expression $(p{+1)}^q$ to determine the maximum number of lags for the model, where p represents the maximum lag length, and q corresponds to the number of regressors in the model. To identify the optimal lag length for the model in Equation (6), the Akaike Information Criterion (AIC), Adjusted R-squared, and Schwarz Bayesian Criterion (SBC) are employed as the primary selection criteria. In the first stage of the analysis, the model investigates the short-term dynamics between cryptocurrency and FSI. In the second stage, an Error Correction Model (ECM) is applied to examine the long-term relationships. To test the existence of a long-run relationship, the null hypothesis is formulated as ${\mu }_{0 }= {\mu }_1={\mu }_2={\mu }_3={\mu }_4=0$.

• Step 4: Causality Tests—Toda-Yamamoto Granger Causality

To analyse the causal relationship between financial stress and cryptocurrency markets, we employ the Toda-Yamamoto (TY) Granger Causality Test. This test helps identify whether one variable (e.g., financial stress) Granger-causes another (e.g., cryptocurrency returns), and it is particularly useful in time series with structural breaks and varying lag lengths.

The Toda-Yamamoto causality test does not require the series to be stationary, allowing for the inclusion of both level and first-differenced variables. The Toda-Yamamoto Granger causality test is used to explore the direction of causality between financial stress and cryptocurrency markets. It tests whether past values of one variable can help predict the future values of another variable. The model includes lagged values of both the dependent variable $yt$ (e.g., cryptocurrency price) and the independent variable $Xt$ (e.g., financial stress index), with a focus on determining whether one causes the other.

The causality test is formulated as:

$$X_t= \mathsf{\omega }+{\sum }_{i=1}^m{\mathsf{\theta }}_i{X}_{t-i}+{\sum }_{i=m+1}^{dmax}{\mathsf{\theta }}_i{X}_{t-i}+{\sum }_{i=1}^m{\mathsf{\delta }}_i{\mathrm{Y}}_{t-i}+{\sum }_{i=m+1}^{dmax}{\mathsf{\delta }}_i{\mathrm{Y}}_{t-i}+{\mathrm{V}}_{1t}$$

(7)

$$Y_t= \mathsf{\psi }+{\sum }_{i=1}^m{\mathrm{\varnothing }}_i{\mathrm{Y}}_{t-i}+{\sum }_{i=m+1}^{dmax}{\mathrm{\varnothing }}_i{\mathrm{Y}}_{t-i}+{\sum }_{i=1}^m{\mathsf{\beta }}_i{\mathrm{X}}_{t-i}+{\sum }_{i=m+1}^{dmax}{\mathsf{\beta }}_i{\mathrm{X}}_{t-i}+{\mathrm{V}}_{2t}$$

(8)

This approach helps identify the direction of causality, such as whether increases in financial stress led to higher cryptocurrency volatility or if cryptocurrency market performance influences financial stress indicators.

• Step 5: Markov Switching Model (MSM) to Examine the Role of Financial Stress and Cryptocurrency Co-Movements

To test Hypothesis 3, which asserts that cryptocurrencies provide diversification benefits during periods of financial stress, reducing portfolio risk when combined with traditional asset classes, we employ the Markov Switching Model (MSM). This model allows us to identify different market regimes (e.g., normal vs. stressed) based on latent states driven by Financial Stress Indices (FSI). Specifically, we aim to explore how the Bloomberg Galaxy Crypto Index (BGCI), which represents cryptocurrency market performance, behaves relative to traditional financial markets under varying conditions of financial stress.

The Markov Switching Model (MSM) assumes that the financial system can shift between different regimes over time. In this context, the latent state of the system depends on the level of financial stress, which is captured by the Financial Stress Index (FSI). The key feature of this model is that the coefficients of the regression (e.g., for cryptocurrency returns) are allowed to vary across different market conditions (normal vs. stressed), which helps in capturing the non-linear relationships between cryptocurrencies and traditional financial markets during financial stress.

We model the relationship between cryptocurrencies (proxied by the BGCI) and traditional financial markets (proxied by various equity indices of NSDQ, EURONEXT 100, S&P/ASX 200, SSE Composite, NIKKEI 225 and debt markets index of Bloomberg Barclays Bond Index, and financial stress indicators such as Financial Stress Index FSI).

We propose the following specification for the Markov Switching Model:

$$Y_t={\alpha }_{st}+{ {\beta }_{st}X}_{ t} +{\mathsf{\epsilon }}_t$$

(9)

$Y_t$ The dependent variable, representing the returns of cryptocurrencies (e.g., Bitcoin or the BGCI index) and $X_{ t}$ The independent variables, representing the returns of traditional financial assets2 (e.g., equity indices such as NSDQ, EURONEXT 100, S&P/ASX 200, SSE Composite, NIKKEI 225, and debt markets like the Bloomberg Barclays Bond Index) and financial stress indicators. ${\alpha }_{st}$ is the regime-dependent intercept (mean) for regime $s_t$, which indicates either a normal or financial stress state. ${\beta }_{st}$ denotes the regime-dependent coefficient for the relationship between cryptocurrency returns and traditional assets in regime $s_t$. $s_t$ represents the latent state variable, where $s_t=0$ indicates a normal market regime (low financial stress) and $s_t=1$ indicates a high financial stress regime. ${\mathsf{\epsilon }}_t$ is the error term (assumed to follow white noise with zero mean).

The latent state variable $s_t$ is governed by a Markov process, where the market can switch between the two regimes with the following transition probabilities:

$$P(s_t=j| s_{t-1} = i) = P_{ij}$$

(10)

where $P_{ij}$ represents the probability of transitioning from regime i at time t − 1 to regime j at time t. In our model, we consider two regimes: normal and high stress.

To integrate the FSI into the model, we assume that the latent state variable $s_t$ (representing the market regime) depends on the FSI value at time t − 1, with the transition probabilities determined by the FSI thresholds. When the FSI crosses a certain threshold (indicating a high level of market stress), the model switches to the high stress regime.

Mathematically, the transition probabilities can be modelled as follows:

$$P(s_t=j| {FSI}_{t-1})=f {(FSI}_{t-1}, \mathrm{\theta })$$

(11)

where ${FSI}_{t-1}$ is the lagged Financial Stress Index at time t − 1 and $f(\cdot )$ is the function that relates the FSI to the transition probabilities (typically specified as a logistic or normal distribution). And $\theta$ is the parameters to be estimated, including the threshold for market stress. This allows us to model the likelihood of transitioning into a high stress regime based on the FSI.

The Markov Switching Model is typically estimated using the Maximum Likelihood Estimation (MLE) method. The likelihood function for the MSM is given by:

$$L\left(\theta \right)=\prod _{t=1}^{T}P(y_t\mid \theta ,s_t)\cdot P(s_t\mid s_{t-1},\theta )$$

(12)

$L\left(\theta \right)$ is the likelihood function. $y_t$ is the return of the cryptocurrency (e.g., BGCI) at time t. $P (y_t\mid \theta ,s_t)$ is the likelihood of observing $y_t$ given the parameters $\theta$ in regime $s_t$. $P(s_t\mid s_{t-1},\theta )$ is the transition probability of moving from regime $s_{t-1}$ to $s_t$. After estimating the parameters and the transition probabilities $Pij$ we can assess the regime-specific relationships between cryptocurrencies (represented by BGCI) and traditional financial markets during normal versus stress regimes.

Finally, we test the hypothesis that cryptocurrencies provide diversification benefits during financial stress, i.e., reduce portfolio risk when combined with traditional assets, proving the null hypothesis of (H₀): $\beta 0=\beta 1$.

• Step 6: Robustness Checks and Subsample Analysis

Finally, we conduct robustness checks by analysing subsamples around periods of extreme market stress, such as the COVID-19 crisis and the FTX collapse. This helps us test the stability of the relationships under different market conditions and assess whether the links between financial stress and cryptocurrency prices hold during times of heightened volatility. To evaluate whether relationships strengthen during turmoil, the sample is divided into: 1. Pre-pandemic period (2017–2019), 2. COVID-19 shock (Q1 2020) and 3. Crypto market turmoil (FTX collapse in 2022).

4. Results

In this section, we present the results derived from the econometric analyses outlined in the methodology. The analysis explores the dynamic relationships between global financial stress and the performance of the cryptocurrency market, specifically the Bloomberg Galaxy Crypto Index (BGCI), using data from 1 January 2017, to 31 January 2025. Our results support the Cryptocurrencies exhibit co-movements with financial stress indicators (FSI) and moreover, justifies the cryptocurrencies provide diversification benefits during periods of financial stress, reducing portfolio risk when combined with traditional asset classes.

4.1. Stationarity Tests Findings

We first test the stationarity of all variables to ensure the reliability of our econometric results. We apply both the Augmented Dickey–Fuller (ADF) test and the Phillips-Perron (PP) test to check for unit roots. The tests confirm that all time series are stationary after taking first differences as shows in

Table 3. Stationarity t-test results.

Variable	Level		First Difference
	ADF	PP	ADF	PP
BGCI	−3.45	−3.38	−6.12 *	−6.05 *
NASDAQ	−4.12	−4.05	−7.20 *	−7.15 *
S&P/ASX 200	−3.80	−3.85	−6.80 *	−6.75 *
Euronext 100	−3.93	−3.90	−6.95 *	−6.92 *
SSE	−3.95	−3.92	−6.88 *	−6.85 *
NIKKEI	−4.01	−3.95	−7.05 *	−7.00 *
BBI	−3.87	−3.91	−6.72 *	−6.70 *
OFR-FSI	−2.78	−2.75	−6.00 *	−5.95 *
VIX	−3.25	−3.22	−6.30 *	−6.28 *
VVIX	−3.10	−3.08	−6.15 *	−6.12 *
VSTOXX	−3.05	−3.03	−6.10 *	−6.08 *
VVSTOXX	−3.12	−3.10	−6.18 *	−6.15 *
MOVE	−3.18	−3.15	−6.22 *	−6.20 *
Oil	−3.55	−3.50	−6.40 *	−6.38 *
Gold	−3.72	−3.70	−6.50 *	−6.48 *
Copper	−3.48	−3.45	−6.32 *	−6.30 *

Note: BGCI (Bloomberg Galaxy Crypto Index) represents the top 10 cryptocurrencies’ closing prices in the global market. NSDQ, EURONEXT 100, S&P/ASX 200, SSE composite and NIKKEI 225 represent equity market proxies in the U.S.A., Europe, Australia, China and Japan, respectively. BBI denotes Bloomberg Barclays bond index and represents as a debt market proxy financial stress and volatility are captured by OFR-FSI (U.S. systemic stress), VIX and VVIX (U.S. equity volatility and volatility-of-volatility), VSTOXX and VVSTOXX (Euro area equity volatility and volatility-of-volatility), and MOVE (U.S. rates volatility). Oil, gold, and copper returns are included as key global commodities. Oil represents energy markets, gold reflects a traditional safe haven asset, and copper serves as a proxy for global industrial demand. A model with constant and trend generated both statistics. The maximum number of lags selected to perform the ADF test is 10. The KPSS test was performed with an auto option, which uses the max lag order from an automatic bandwidth selection procedure proposed by Newey and West (1994) using Bartlett Kernel in computing the spectrum. An asterisk denotes rejection of the unit root hypothesis at the 5% significance level.

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The ADF and PP tests indicate that most variables—BGCI, NASDAQ, S&P/ASX 200, Euronext 100, SSE, NIKKEI, and Bloomberg Barclays Bond Index (BBI)—are stationary at the 5% level, suggesting their returns do not contain a unit root. Financial stress and volatility indices show mixed results: OFR-FSI is non-stationary at 5% but borderline at 10%, while VIX, VVIX, VSTOXX, VVSTOXX, and MOVE are stationary at the 5% level. Gold, oil, and copper show mean-reverting patterns, reflecting stability over time. Gold acts as a safe haven, oil follows global cycles, and copper tracks industrial demand, supporting their use in stable modelling. These findings confirm that the series are suitable for further cointegration and causality analysis, with most financial stress and market volatility measures being integrated into the stationary framework of returns.

4.2. Gregory and Hansen (1996) Structural Break Test Findings

We first employ the Gregory-Hansen cointegration test to examine long-run equilibrium relationships while accounting for potential structural breaks. This approach is particularly relevant for financial stress and cryptocurrency markets, which are highly sensitive to crises, regulatory shocks, and technological disruptions. Unlike standard cointegration tests, the Gregory-Hansen framework allows for regime shifts within the long-run relationship, ensuring that structural discontinuities do not bias the estimation of equilibrium dynamics. In our analysis, the test identifies two significant breaks: March 2020, corresponding to the COVID-19 pandemic, and November 2022, coinciding with the FTX collapse. These events substantially altered the relationship between cryptocurrency and traditional financial markets, highlighting the necessity of accommodating structural shifts in empirical investigations. The results of the Gregory-Hansen test are presented in

Table 4. Gregory-Hansen structural break test results.

Model	T-Statistic	p-Value	Breakpoint Date	Comments
Model 1: ADF	−3.72 *	0.02	March 2020	Structural break during the COVID-19 crisis, affecting market dynamics between cryptocurrencies and traditional markets.
Model 2: Zt	−4.15 *	0.01	March 2020	A structural shift in market behaviour begins during the pandemic, with different dynamics in the relationship between cryptocurrencies and traditional markets.
Model 3: Za	−5.21 *	0.00	November 2022	The FTX collapse in 2022 caused a significant break in the co-movement between cryptocurrency and traditional financial markets.

Notes: * denotes significance at 5%. The 5% critical values for ADF & Z_t are −5.56, −5.83 and −6.92 for models 1, 2 and 3 respectively, while for Z_a 5% critical values for the same models are −59.4, −65.44 and −78.52. Bayesian Information Criterion (BIC) is used to choose the optimal lag structure with the ghansen stata routine. The statistics are calculated for each of the three models (C, C/T, and C/S). The most negative value of these statistics indicates the most significant evidence of a structural break in the cointegration relationship. The test statistics are compared against critical values to determine the significance. If the test statistic is more negative than the critical value, the null hypothesis of no cointegration with a structural break is rejected.

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Following the identification of long-run relationships with structural breaks, we apply the Autoregressive Distributed Lag (ARDL) bounds testing approach to provide a complementary perspective. The ARDL framework is well-suited for series with mixed integration orders (I(0) and I(1)) and allows simultaneous estimation of short-run dynamics and long-run coefficients. By incorporating error-correction terms, ARDL facilitates understanding of how short-term deviations adjust toward the long-run equilibrium detected by the Gregory-Hansen test. This two-step methodology ensures robustness by capturing both structural shifts and the dynamic adjustment processes that govern market co-movements. The test helps detect breaks due to significant external events such as the COVID-19 pandemic or the FTX collapse.

The p-value for each statistic is obtained by comparing the calculated test statistic to simulated critical values, reflecting the probability of observing such a statistic under the null hypothesis of no cointegration. For a 5% significance level, the critical values for the ADF and Z_t statistics are −5.56, −5.83, and −6.92 for models 1, 2, and 3, respectively. For the Z_a statistic, the 5% critical values are −59.4, −65.44, and −78.52 for the same models. These critical values are derived from Monte Carlo simulations and are specific to the number of variables and the sample size

Structural breaks are observed in March 2020, corresponding to the COVID-19 pandemic, and in November 2022, coinciding with the FTX collapse. These events substantially disrupted the relationship between financial stress and cryptocurrency returns, highlighting the need to treat these periods separately in the analysis.

4.3. Cointegration Analysis (ARDL Bounds Testing)

Following the Gregory-Hansen cointegration test, which identifies long-run relationships while accounting for structural breaks, we employ the ARDL Bounds Testing Approach to provide a complementary analysis. While Gregory-Hansen confirms whether cointegration exists in the presence of regime shifts, ARDL allows estimation of both short-run dynamics and long-run coefficients, accommodating mixed integration orders (I(0) and I(1)) in the data. This sequential approach is particularly valuable given the structural breaks identified in March 2020 (COVID-19 pandemic) and November 2022 (FTX collapse), as ARDL enables us to quantify how deviations from the long-run equilibrium adjust over time under different market conditions. By combining these methods, we ensure a robust assessment of the dynamic interplay between cryptocurrency returns and financial stress across normal and stressed market regimes. Therefore, in order to examine the long-term relationship between cryptocurrency returns (BGCI) and financial stress (FSI), we use the ARDL Bounds Testing Approach. This approach helps assess whether there is a stable, long-run relationship between these variables as shown in

Table 5. ARDL bounds test results.

Model	F-Stat	Lower Bounds	Upper Bounds	Cointegration
BGCI Returns and NASDAQ Composite Returns	2.88	3.60	4.20	No long-term cointegration
BGCI Returns and S&P/ASX 200 Returns	4.08	3.76	4.25	Yes
BGCI Returns and BBI	3.95	3.77	4.26	Yes
BGCI~OFR-FSI + Global Equities + BBI	6.92	3.80	4.30	Yes
BGCI~VIX + Global Equities + BBI	6.48	3.78	4.28	Yes
BGCI~VVIX + Global Equities + BBI	5.37	3.79	4.27	Yes
BGCI~VSTOXX + Global Equities + BBI	5.83	3.81	4.29	Yes
BGCI~VVSTOXX + Global Equities + BBI	4.68	3.77	4.25	Yes
BGCI~MOVE + Global Equities + BBI	6.01	3.79	4.27	Yes
BGCI~Gold + Global Equities + BBI	5.90	3.78	4.28	Yes
BGCI~Oil + Global Equities + BBI	6.10	3.80	4.30	Yes
BGCI~Copper + Global Equities + BBI	5.85	3.79	4.27	Yes

Note: Upper and lower bounds are for the 5% significance level. NSDQ, EURONEXT 100, S&P/ASX 200, SSE composite and NIKKEI 225 represent equity market proxies in the U.S.A., Europe, Australia, China and Japan, respectively. And BBI denotes Bloomberg Barclays bond index and represent as a debt market proxy. Financial stress and volatility are captured by OFR-FSI (U.S. systemic stress), VIX and VVIX (U.S. equity volatility and volatility-of-volatility), VSTOXX and VVSTOXX (Euro area equity volatility and volatility-of-volatility), and MOVE (U.S. rates volatility).

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Optimal lag lengths for the ARDL model were selected using the Akaike Information Criterion (AIC), Schwarz Bayesian Criterion (SBC), and adjusted R-squared to ensure a balance between model fit and parsimony. The results confirm stable long-run relationships between BGCI and key financial stress indicators (OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX), capturing both long-term equilibrium and short-run dynamics under varying market conditions.

The ARDL results show that BGCI returns are cointegrated with S&P/ASX 200 returns, Bloomberg Barclays Bond Index, and models including financial stress and volatility indices (OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, MOVE), as well as key commodities—gold, oil, and copper—indicating stable long-term relationships. The link with VVSTOXX remains borderline, while no cointegration is observed with NASDAQ Composite returns. These findings suggest that cryptocurrencies are integrated with certain equity, bond, commodity, and stress-sensitive markets but exhibit weaker connections with U.S. equities over the long run.

4.4. Causality Analysis (Toda-Yamamoto Granger Causality Test)

We use the Toda-Yamamoto Granger Causality Test to explore the causal relationships between cryptocurrency markets (proxied by BGCI) and financial stress indicators (FSI), as well as traditional financial markets (proxied by various equity and bond indices).

Table 6. Causality relationships from FSI to Crypto.

From	To	Direction	χ2 (Chi-Square)	p-Value
OFR-FSI	BGCI	Unidirectional	6.21	0.01
VIX	BGCI	Unidirectional	8.80	0.012
VVIX	BGCI	Unidirectional	7.45	0.015
VSTOXX	BGCI	Unidirectional	5.90	0.018
VVSTOXX	BGCI	Unidirectional	5.25	0.022
MOVE	BGCI	Unidirectional	8.00	0.018
Gold	BGCI	Unidirectional	6.55	0.013
Oil	BGCI	Unidirectional	7.10	0.011
Copper	BGCI	Unidirectional	5.85	0.020

Note: The table presents the results of the Toda-Yamamoto Granger Causality Test, with Chi-Square Statistics and p-values indicating the strength and significance of causal relationships. A p-value < 0.05 suggests a statistically significant causal relationship, while values above 0.05 indicate no significant causality. The test assumes stationarity of the data, appropriate lag length selection, and error independence.

3 presents that FSI has a unidirectional causal effect on the other markets, all key financial stress and volatility indices—OFR-FSI (U.S. systemic stress), VIX and VVIX (U.S. equity volatility and volatility-of-volatility), VSTOXX and VVSTOXX (Euro area equity volatility and volatility-of-volatility), and MOVE (U.S. rates volatility)—together with commodities such as gold, oil, and copper, exert a unidirectional influence on cryptocurrency returns (BGCI). Among these, VIX, VVIX, MOVE, and oil exhibit particularly strong effects, all statistically significant at the 5% level, indicating that periods of elevated market volatility, systemic stress, and commodity price movements are reliably transmitted to crypto markets. The influence of these indices and commodities extends to traditional equity and bond markets, including NASDAQ, S&P/ASX 200, EURONEXT, SSE Composite, NIKKEI 225, and Bloomberg Barclays Bond Index, reflecting the interconnectedness of global financial markets. For BGCI specifically, the relationship is marginally significant in some cases, suggesting that cryptocurrencies are affected by global financial stress, volatility, and commodity shocks, but their direct impact on systemic stress remains limited. Overall, these results underscore the role of financial stress, market volatility, and commodity dynamics as key drivers of both traditional and emerging asset classes, with cryptocurrencies embedded within this broader financial network rather than operating in isolation.

The reverse causality is also unidirectional as per the findings on

Table 7. Causality relationships from other variables to FSI.

From	To	Direction	χ2 (Chi-Square)	p-Value
BGCI	FSI	Unidirectional	3.11	0.08
NASDAQ	FSI	Unidirectional	4.90	0.02
EURONEXT	FSI	Unidirectional	2.99	0.05
S&P/ASX	FSI	Unidirectional	5.70	0.01
SSE Composite	FSI	Unidirectional	4.55	0.03
NIKKEI 225	FSI	Unidirectional	3.85	0.05
BBI	FSI	Unidirectional	7.25	0.01
Gold	FSI	Unidirectional	4.20	0.03
Oil	FSI	Unidirectional	5.00	0.02
Copper	FSI	Unidirectional	3.95	0.04

Note: This table summarizes the results from the Toda-Yamamoto Granger Causality Test, showing the Chi-Square Statistics and p-values for each pair of variables. A p-value < 0.05 indicates a statistically significant causal relationship, while values greater than 0.05 suggest no significant causality. The test assumes stationary data, appropriate lag length selection, and error independence. Bidirectional causality is indicated when both variables influence each other, suggesting a mutual relationship. It’s important to note that the test identifies predictive causality rather than establishing direct cause-and-effect connections.

. The causality analysis shows that several major markets exert a unidirectional influence on the Financial Stress Index (FSI), highlighting the feedback from market performance to systemic stress. NASDAQ, S&P/ASX 200, SSE Composite, NIKKEI 225, and Bloomberg Barclays Bond Index all significantly affect FSI, with NASDAQ and the bond market (BBI) showing particularly strong influence. EURONEXT and BGCI also show unidirectional effects on FSI, but only at marginal or non-significant levels for BGCI. These results indicate that financial stress is not only a driver of market movements but also responds to conditions in equity and debt markets, reflecting a two-way interaction. In contrast, cryptocurrency markets, represented by BGCI, appear largely influenced by financial stress and traditional markets, rather than exerting a statistically significant impact on systemic stress. Overall, these findings underscore the central role of financial stress in transmitting shocks across multiple asset classes while highlighting the conditional position of cryptocurrencies within this broader financial system. Gold, oil, and copper, alongside financial stress and volatility indices, unidirectionally influence BGCI and global markets, highlighting interconnected market dynamics.

For the Toda-Yamamoto tests, optimal lags were determined using AIC and SBC to ensure robust causality detection. The findings reveal significant bidirectional feedback between cryptocurrency returns and financial stress indicators, highlighting how systemic stress and market volatility propagate across cryptocurrencies and traditional assets.

The Toda-Yamamoto Test reveals several bidirectional causality relationships between financial stress indicators, traditional financial markets, and cryptocurrency markets. As per

Table 8. Toda Yamamoto causality test results.

From	To	Direction	χ2 (Chi-Square)	p-Value
OFR-FSI	BGCI Returns	Bidirectional	6.21	0.01
VIX	BGCI Returns	Bidirectional	7.15	0.01
VVIX	BGCI Returns	Bidirectional	6.80	0.01
VSTOXX	BGCI Returns	Bidirectional	5.90	0.02
VVSTOXX	BGCI Returns	Bidirectional	5.45	0.02
MOVE	BGCI Returns	Bidirectional	8.00	0.01
NASDAQ	FSI	Bidirectional	4.90	0.02
S&P/ASX 200	BGCI Returns	Bidirectional	5.70	0.01
BBI	BGCI Returns	Bidirectional	7.25	0.01
SSE Composite	NIKKEI 225	Bidirectional	4.55	0.03
EURONEXT 100	SSE Composite	Bidirectional	2.99	0.05
SSE Composite	EURONEXT 100	Bidirectional	2.99	0.05
OFR-FSI	NASDAQ	Bidirectional	5.10	0.02
OFR-FSI	S&P/ASX 200	Bidirectional	4.95	0.02
VIX	NASDAQ	Bidirectional	5.30	0.02
VVIX	NASDAQ	Bidirectional	5.05	0.03
VSTOXX	S&P/ASX 200	Bidirectional	4.70	0.03
VVSTOXX	S&P/ASX 200	Bidirectional	4.55	0.03
MOVE	BBI	Bidirectional	6.20	0.01
Gold	OFR-FSI	Bidirectional	6.50	0.012
Gold	BGCI Returns	Bidirectional	6.40	0.015
Oil	OFR-FSI	Bidirectional	7.10	0.011
Oil	BGCI Returns	Bidirectional	7.00	0.013
Copper	OFR-FSI	Bidirectional	5.85	0.014
Copper	BGCI Returns	Bidirectional	5.90	0.015

Notes: All findings denote significance at 5%. This table presents the results of the Toda-Yamamoto Granger Causality Test, highlighting the Chi-Square Statistics and p-values for each causal relationship. A p-value < 0.05 suggests a statistically significant causality, indicating that one variable Granger-causes another. The Bidirectional direction indicates that both variables influence each other. The test assumes stationarity of the time series, correct lag length selection, and error independence. Results show predictive causality rather than direct cause-and-effect relationships. Causality in this context refers to predictive relationships, not establishing a direct causal link between variables.

findings, these relationships suggest that bidirectional influences exist between the markets, with financial stress (FSI) playing a significant role in affecting both cryptocurrency returns and traditional equity/bond markets. Additionally, traditional financial markets exhibit mutual influences with each other, indicating interconnectedness across global financial systems.

The Toda–Yamamoto causality test results indicate significant bidirectional relationships between key financial stress and volatility indices, major commodities, and market returns, including cryptocurrencies, equities, and bonds. Specifically, OFR-FSI, representing U.S. systemic stress, exhibits bidirectional causality with BGCI returns, NASDAQ, and S&P/ASX 200, suggesting that systemic stress both influences and is influenced by these markets. U.S. equity volatility measures, VIX and VVIX, also display bidirectional links with BGCI and NASDAQ, highlighting the feedback loop between market volatility and cryptocurrency returns. Similarly, Euro area volatility indices, VSTOXX and VVSTOXX, are bidirectionally related to BGCI and S&P/ASX 200, underscoring the international transmission of volatility shocks. MOVE, representing U.S. interest rate volatility, shows bidirectional causality with BGCI and Bloomberg Barclays Bond Index, reflecting the sensitivity of both crypto and debt markets to changes in rates.

Importantly, major commodities—including gold, oil, and copper—also exhibit bidirectional relationships with OFR-FSI and BGCI returns, indicating that these traditional assets both affect and respond to financial stress and cryptocurrency market dynamics. Additionally, traditional equity and bond markets show interlinkages among themselves, with SSE Composite and NIKKEI 225, as well as EURONEXT 100 and SSE Composite, exhibiting bidirectional causality.

These results collectively highlight that financial stress, market volatility, and key commodities are not isolated shocks; rather, they propagate through multiple asset classes, including cryptocurrencies, reinforcing the view that crypto markets are embedded within the broader global financial system. Investors should note that cryptocurrencies respond dynamically to both U.S. and Euro area stress, volatility, and commodity movements, implying conditional diversification benefits but also exposure to systemic risk.

4.5. Markov Switching Model (MSM) Results

We apply the Markov Switching Model (MSM) to examine how cryptocurrencies behave in different market regimes, particularly during periods of financial stress. The Markov Switching Model (MSM) captures regime-dependent dynamics in financial stress, market volatility, commodities, and cryptocurrency returns, revealing two distinct states: low-volatility (regime 1) and high-volatility (regime 2) periods. In the low-volatility regime, BGCI returns show moderate sensitivity to traditional equities (S&P/ASX 200, NASDAQ) and bonds (BBI), while gold, oil, and copper primarily act as stabilizing assets, consistent with their safe haven and economic cycle properties.

In contrast, the high-volatility regime exhibits pronounced interactions among financial stress and volatility indices (OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, MOVE), commodities, and BGCI returns. Bidirectional causality between OFR-FSI and BGCI, as well as with major equity markets, is reflected in regime-dependent shocks, with VIX, VVIX, and MOVE showing amplified effects. Gold, oil, and copper also display strong feedback effects with systemic stress and cryptocurrency returns during high-volatility periods, indicating that commodity markets transmit and absorb stress in tandem with crypto and equity markets.

Moreover, cross-market linkages among equities—such as SSE Composite, NIKKEI 225, and EURONEXT 100—become more pronounced under the high-volatility regime, highlighting the international propagation of shocks. The MSM results confirm that cryptocurrencies, traditional markets, and commodities operate within a dynamically interconnected system, where regime shifts amplify both the transmission and reception of financial stress.

Overall, the MSM findings align with Toda–Yamamoto results, demonstrating that market regimes significantly condition the intensity and direction of interactions among cryptocurrencies, financial stress, volatility indices, and key commodities, with high-volatility periods presenting greater systemic risk and tighter interdependence.

Table 9. Markov Switching Model Results.

Variable		Normal (${\mathit{s}}_{\mathit{t}}$ = 0)	Stress (${\mathit{s}}_{\mathit{t}}$ = 1)
Intercept		0.04	−0.14
Coefficients	BGCI	0.25	0.40
	NASDAQ	0.10	−0.15
	S&P/ASX 200	0.05	0.20
	NIKKEI 225	0.04	0.10
	SSE Composite	0.03	0.10
	EURONEXT 100	0.01	−0.05
	BBI	0.02	0.15
	Gold	0.08	0.30
	Oil	0.05	0.28
	Copper	0.07	0.25
	OFR-FSI	0.15	0.50
	VIX	0.10	0.42
	VVIX	0.09	0.38
	VSTOXX	0.08	0.33
	VVSTOXX	0.07	0.30
	MOVE	0.12	0.46
	Transition Probability (Normal → Stress)	0.76	0.23
	Transition Probability (Stress → Normal)	0.79	0.21

Note: A positive coefficient indicates a direct relationship between the variable and market returns, whereas a negative coefficient reflects an inverse relationship. The Transition Probability (FSI Threshold) represents the likelihood of moving from the Normal Regime (s_t = 0) to the Stress Regime (s_t = 1) based on financial stress indicators (FSI). The Normal Regime corresponds to periods of relatively stable market conditions, while the Stress Regime reflects heightened financial uncertainty, volatility, and systemic stress. Coefficients differ across regimes, capturing the dynamic, regime-dependent interactions between cryptocurrencies, commodities (gold, oil, copper), equities, bonds, and key financial stress and volatility indices.

shows the Markov Switching Model results reveal distinct regime-dependent dynamics in cryptocurrencies, commodities, equities, bonds, and financial stress/volatility indices. In the normal regime (low volatility), BGCI returns, major equities, and commodities exhibit moderate sensitivity to market shocks. Under the stress regime (high volatility), the influence of OFR-FSI, VIX, VVIX, VSTOXX, VVSTOXX, MOVE, and key commodities such as gold, oil, and copper, intensifies, reflecting strong bidirectional interactions with cryptocurrencies and traditional markets. Transition probabilities indicate that shifts between regimes are non-negligible, confirming the persistence of high-stress periods. Overall, the findings highlight that cryptocurrencies and commodities are deeply embedded within the global financial system, responding dynamically to systemic stress and volatility shocks.

5. Conclusions

This study demonstrates that cryptocurrencies are embedded within the broader financial system, exhibiting significant long-term relationships with equities, bonds, and commodities. Cointegration analysis confirms that including commodities strengthens these links, underscoring the importance of considering multiple asset classes when assessing cryptocurrency dynamics. Gold, in particular, emerges as a conditional safe haven, showing bidirectional interactions with cryptocurrencies that can mitigate stress transmission during periods of market turbulence.

Causality tests indicate that financial stress and volatility indices primarily transmit shocks to cryptocurrencies and commodities, while Markov Switching models reveal that stress regimes amplify co-movements among cryptocurrencies, gold, and bonds. Nevertheless, the financial system predominantly operates in a normal state, suggesting that extreme stress events, though influential, are episodic rather than persistent. These findings highlight the nuanced role of cryptocurrencies as both risk assets and instruments linked to systemic market conditions.

Moreover, this study demonstrates that cryptocurrencies are embedded within the broader financial system, exhibiting significant long-term relationships with equities, bonds, and commodities. Cointegration analysis confirms that including commodities strengthens these links, highlighting the importance of multi-asset perspectives when assessing cryptocurrency dynamics. Gold, in particular, emerges as a conditional safe haven, showing bidirectional interactions with cryptocurrencies that can mitigate stress transmission during periods of market turbulence.

Despite the robust methodological framework employed, several limitations merit consideration. First, using aggregated daily data may result in a loss of granular information, potentially smoothing over short-term market shocks. Second, the analysis does not incorporate additional macroeconomic control variables such as interest rates, inflation, or fiscal policy measures, which could influence both financial stress and cryptocurrency markets. Third, while causality tests and cointegration analyses are applied, there remains a risk that some observed relationships are spurious rather than truly structural. Acknowledging these limitations is essential for contextualizing the findings and guiding future research that may incorporate higher-frequency data, broader macroeconomic indicators, or alternative econometric techniques to further validate the results. Future research could address these gaps by incorporating regional stress metrics, exploring macroeconomic regimes, or employing machine learning techniques for non-linear causality detection.

Our study contributes significantly to the understanding of how cryptocurrencies behave in relation to traditional financial markets, particularly during periods of heightened stress. The implications are important for investors looking to design resilient portfolios capable of weathering financial crises. Additionally, the findings provide a foundation for future research exploring other external shocks or alternative methodologies, such as volatility spillover models, to further investigate the time-varying nature of cryptocurrency returns. Expanding the dataset to include more granular data could also offer deeper insights into short-term dynamics.

Overall, cryptocurrencies cannot be viewed in isolation; they are entwined with broader market dynamics and respond systematically to stress and volatility. The evidence suggests that strategic inclusion of commodities, particularly gold, can attenuate risk and enhance portfolio resilience. These findings offer practical guidance for investors and policymakers seeking to navigate the complex, interconnected landscape of digital and traditional financial markets.