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This study investigates how geopolitical risk moderates the relationship between investor attention and stock market volatility in both emerging and developed markets. To achieve this objective, the GARCH-MIDAS model is employed to decompose daily market returns into short- and long-term volatility components. The Google Search Volume Index is used as a proxy for investor attention along with country-specific geopolitical risk indices which are assessed for the period spanning from 2014 to 2023. The findings reveal that the effect of investor attention on stock market volatility is not uniform but instead varies across and within developed and emerging markets. Furthermore, GPR is found to be a crucial factor that can either weaken, magnify, or change the nature of the relationship between investor attention and volatility depending on the surveyed economy. The findings highlight the critical role of geopolitical risk in shaping market dynamics, suggesting that both investors and policymakers should incorporate geopolitical factors in risk management and portfolio strategies. The study contributes to existing literature by providing a novel perspective on how geopolitical risk moderates the relationship between investor attention and market volatility, utilizing a comparative analysis across different economic regions, which has not been done before.

Long memory suggests that past returns can influence future returns over extended periods, indicating potential predictability. The aim of this study was to empirically examines the interplay between long memory effects, downside risk, and stock returns across five major international equity markets (S&P 500, FTSE 100, Nikkei 225, DAX, and ASX) from 2000 to 2022. An ARFIMA model which quantify fractional differencing was used in conjunction with a correlation matrix, regression and Granger causality test to investigate the interplay. The findings revealed a significant long memory across all markets, with Nikkei 225 exhibiting the strongest persistence, attributed to Japan’s prolonged economic stagnation. Counterintuitively, lagged downside risk positively predicts returns, aligning with behavioural theories of investor overreaction to tail events. Bidirectional causality between risk and returns underscores reflexive market dynamics. The study bridges a critical gap by integrating long memory into downside risk models, demonstrating that persistent volatility amplifies tail risk premiums. The findings of this study suggest that financial market regulators need to seriously considers adaptive regulatory tools due to the dual long memory in returns and downside risk necessitates. To the author´s knowledge, this study is the first to bridge a critical gap in the literature by systematically integrating long memory effects with downside risk metrics so as to provide a more robust framework for understanding risk-return dynamics, as it accounts for the persistent nature of volatility and tail risk, which traditional short-memory models often overlook.

Financial markets are a system of complex price dynamics that are often influenced by various nonlinear factors. Traditional linear models such as Autoregressive Moving Average also known as ARMA and the GARCH model often fail to capture the inherent nonlinearities observed in financial market returns and trading volumes which poses significant problems in modelling financial time series. The aim of this study was to investigates the role of threshold nonlinearity in modelling financial market returns and trading volume. Daily share prices and trading volumes from the S&P 500 and the Nasdaq indices spanning from January 2000 to December 2020 were used as the sample financial markets. The findings revealed that the threshold model improves predictive performance over traditional linear models, highlighting the importance of incorporating nonlinearity for understanding the dynamics of financial markets. A threshold autoregressive model was proposed to account for sudden shifts in market conditions and nonlinear dependencies between returns and trading volumes.

Prior research on volatility spillover indicates that financial market spillovers are not uniform across all markets. Their intensity and direction depend on factors such as market size, economic linkages, and the nature of the shock. The aim of this study was to comprehensive investigation of volatility spillovers across five major international equity markets from January 2008 to January 2024, a period encompassing multiple financial crises. Utilizing a conditional volatility model, followed by the construction of a spillover index and Granger causality tests to investigate the direction and magnitude of volatility transmission, the findings of this study revealed that the S&P 500 is a net receiver of volatility, acting as a global shock absorber rather than a primary transmitter. In contrast, European markets and the Nikkei 225 emerged as net transmitters, with a tightly coupled, bidirectional relationship observed between the United Kingdom and European markets. The Shanghai Composite was also found to be nearly neutral, likely due to capital controls. These results reiterated the notion that volatility transmission networks are dynamic and not solely dictated by market size. The findings of this study suggest that asset managers and other investors can significantly increase the value of their portfolios if they adopt a multi-polar risk management framework, moving beyond a United States centric view for international diversification to include more European and Asian markets assets in their portfolios.

Traditional financial models assume constant variance in asset returns however, empirical evidence highlights volatility persistence, which are effectively captured by ARCH and GARCH models. The aim of this study was to examine the heteroskedastic behaviour of stock prices across international financial markets. Using a GARCH (1,1) model with a student’s t-distribution, this study analyses daily stock returns from the NYSE, FTSE 100, Nikkei 225, and Shanghai Composite (SSE) between 2018 and 2023. The findings confirm significant autoregressive conditional heteroskedasticity in all markets, supporting the notion that financial volatility is dynamic and clustered. Developed markets, such as the NYSE and FTSE 100, exhibit lower baseline volatility but more persistent shocks, indicative of market efficiency and stability. In contrast, emerging markets, particularly SSE, demonstrate higher volatility and greater sensitivity to past shocks, reflecting heightened uncertainty. The results re-iterate the importance of incorporating dynamic volatility models in risk assessments. Given the increasing complexity of global financial systems, this study advocates for enhanced regulatory frameworks and adaptive econometric methodologies to account for evolving market structures and external macroeconomic shocks.

Financial markets are a system of complex price dynamics that are often influenced by various nonlinear factors. Traditional linear models often do not capture the inherent nonlinearities that exist between them. The aim of this study was to examine the interconnectedness of global financial markets using a multivariate Granger causality framework, focusing the United States, Europe, Asia, and emerging markets. Daily closing share prices spanning 13 years were utilised (January 2010 to December 2023) to analyze the shock transmission dynamics. The findings revealed unidirectional causality from the U.S. to European, Japanese, and Emerging markets, underscoring its dominant role in global financial networks. Conversely, European and Asian markets exhibit no reverse causality on the United States, highlighting asymmetrical interdependence. Notably, China’s Shanghai Composite Granger-causes Emerging market returns, reflecting its rising influence. These insights challenge conventional models that underestimate multilateral linkages, demonstrating that financial integration has intensified bidirectional interactions between Emerging markets and developed markets. By implication, investors should reassess exposure to dominant markets like the U.S. and China’s growing sway over Emerging economies while policymakers should prioritize cross-border spillover monitoring and systemic risk frameworks to address asymmetrical dependencies. Also, institutions must adopt nonlinear models to better capture shock transmission and evolving interdependencies, enhancing resilience against contagion.

The aim of this study was to investigate phase distribution and phase correlation dynamics across international financial markets to uncover cyclical patterns, synchronization, and contagion effects. The sample financial markets were the S&P 500, DAX, Nikkei 225, FTSE 100, Shanghai Composite, BSE Sensex with daily closing prices ranging from 2018–2023. Using the Hilbert-Huang Transform complemented by Phase Concentration Index, Kuiper tests, and Granger causality, the results reveal distinct phase clustering in the Shanghai and BSE Sensex. Developed markets exhibit lower volatility clustering (S&P 500: 28% high-volatility phases) but stronger cross-market synchronization (S&P-DAX: 0.82 correlation), underscoring their interconnectedness. The S&P 500 emerges as a global anchor, Granger-causing European and Asian markets with 1.8–3.5-day lags. Crisis periods, particularly COVID-19, amplify synchronization (average correlation=0.92), while non-crisis phases show market-specific volatility (correlation=0.65). Emerging markets demonstrate regional co-movement (Shanghai-BSE: 0.73), offering diversification opportunities. The findings highlight the hierarchical structure of global markets, where developed economies drive cycles, while emerging markets remain prone to instability. This study advances phase-based methodologies as tools for systemic risk monitoring, providing insights into crisis contagion and investor strategies balancing short-term synchronization with long-term diversification.

Financial markets areconstantly fluctuating in response to a range of factors. These fluctuations connote volatility which are unpredictable behaviour that deviates significantly from the patterns observed in stable conditions. It is therefore important to use standard stochastic volatility models to capture the time-varying nature of volatility during periods of financial distress in other to make informed decisions. The aim of this study was to explore stochastic volatility in financial markets during periods of financial distress using a Heston model. The sample financial markets were, the CAC 40, the DAX, the JSE, the Nasdaq Index and the Nikkei-225. The 2007/2008 financial crisis and the Covid-19 pandemic were used as sample time frames. The findings of this study revealed extortionate stochastic volatility during the Covid-19 pandemic compared to the 2007/2008 financial crisis. Since the 2007/ 2008 crisis stemmed from a collapse in the financial system, the nature of the event was more localized within the financial sector and had a somewhat more predictable unfolding than the Covid-19 pandemic. By Implication, it may be suggested that it was more difficult to price assets during the Covid-19 pandemic due to extreme uncertainty which resulted in inflated option premiums as investors sought hedging strategies.

Stock return modeling is essential for active investors and market players. Value and risk analysis benefit from these simulations. Despite extensive study on stock price modeling, little is understood about how internal and external shocks affect stock market returns. Therefore, this study sought to fill this gap. A sample of five international financial markets from December 1, 2007, to June 30, 2009 and January 1, 2020 to December 31, 2021, the 2007-2008 financial crisis and most recent COVID-19 pandemic, were tested using a Cramer-von Mises and Watson test. Research showed that internal market volatility is more damaging than external shocks. During financial instability driven by external shocks, portfolio managers should expect two to three standard deviations of volatility. However, financial system shocks should cause a greater range of volatility. The authors believe this is the first study to predict stock market returns in reaction to regulatory announcements from market shocks.

Modelling volatility using asset price returns has always been at the forefront of financial economics and option pricing. Observing the conditional variance properties in these asset returns, can be very useful for trend analysis and volatility predictions which are ever needed for trading, portfolio management and financial decision making. The aim of the study was to model and forecast volatility in stock markets. Six financial markets namely the Nasdaq, JSE, the DAX, the CAC 40 and the Nikkei 225 were used as samples with a sampling frame from January 29, 2018 to January 29, 2023. The findings of this study revealed that the variance for all the financial markets under consideration changes significantly with the passage of time. Also, volatility in the JSE, DAX & CAC 40 display fat tail distributions and it is expected to move by three standard deviations. Accordingly, volatility will persist in the Nasdaq, DAX and CAC 40 at an increasing rate but will persist at a decreasing rate in the JSE and Nikkei 225. Considering the peril involved in stock market investing, this study makes a notable contribution to estimating market volatility which is an integral component of asset pricing. With this knowledge, analyst and market traders will have a better understanding of the error distribution in stock markets which will assist in specifying predictive asset prices.

In the preceding decade, the South African economy has experienced challenges due to global disruptive events, hence, the implementation of risk mitigation strategies becomes a priority in volatile markets. Stable distributions account for skewness and heavy-tailed behaviour which are frequently observed in financial data. This study aims to investigate the fit of stable distributions for three FTSE/JSE indices and the USD/ZAR currency exchange rate. The maximum likelihood method was applied to fit Nolan’s -parameterization stable distribution. Value at Risk (VaR) is measure assessing market risk, therefore, VaR estimates and Kupiec likelihood test are applied to evaluate the extreme tail behaviour of the fitted stable model. Results show the robustness of stable distributions in the long and short position for each daily returns. This research validates the use of stable distributions aimed at capturing the characteristics financial data. Those concerned with curtailing losses and investigating alternatives for financial modeling in the South African financial industry may benefit the most by using stable distributions.

  Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.