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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.

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.

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.

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.

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.

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.