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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.

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.

This study sought to model the stock market return volatility at the Nairobi Securities Exchange (NSE) in the presence of structural breaks. Using daily NSE 20 share index for the period 04/01/2010  to  29/12/2017,  the market return volatility was modeled using different GARCH type models and taking into account four endogenously identified structural breaks. The market exhibited a non-normal distribution that was leptokurtic and negatively skewed and also showed evidence for ARCH effects, volatility clustering, and volatility persistence. We found that by considering structural breaks, volatility persistence was reduced, while leverage effects were found to lead to explosive volatility. In addition, investors were not rewarded for taking up additional risk since the risk premium was insignificant for the full period. However, during explosive volatility, investors were rewarded for taking up more risk. Moreover, we found that risk premium, leverage effects, and volatility persistence were significantly correlated. The GARCH (1,1) and TGARCH(1,1) models were found to be the best fit models to test for symmetric and asymmetric effects respectively. While the GARCH models were able to provide evidence for the stylized facts in the NSE, we conclude that the presence or absence of these features is period specific. This especially relates to volatility persistence, leverage effects, and risk premium effects. Caution should, therefore, be taken in using a specific GARCH model to forecast market return volatility in Kenya. It is thus imperative to pretest the data before any return volatility forecasting is done.

This paper aims to analyze cryptocurrency volatility by examining the effect of Gold, Dollar Index, and Composite Stock Price Index (IHSG) as independent variables and on Bitcoin and Ethereum as dependent variables. The cryptocurrency objects in this study are Bitcoin and Ethereum, which have the largest market capitalization. The data in this study used the period January 1, 2018, to December 31, 2021. This study used GARCH analysis. This study's results indicate that Bitcoin's volatility is influenced by the price of Bitcoin itself, gold, and the stock exchange index, and Ethereum and the stock exchange index influence Ethereum. This shows that the cryptocurrency market is inefficient as the prices are also affected by past prices.

  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.    

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.

This study empirically investigates hierarchical endogeneity and shock transmission among three major international stock markets the S&P 500, FTSE 100, and Nikkei 225 from 2010 to 2023. Utilizing a Vector Autoregression framework and Granger causality test, the research examines the direction and strength of cross-market dependencies. The findings reveal a clear, asymmetric structure where the US market acts as the primary exogenous driver, with unidirectional causality flowing from the S&P 500 to both the FTSE 100 and Nikkei 225. A secondary channel of influence from the UK to Japan was also identified. Forecast error variance decomposition confirms the US market's dominance, explaining over 25% of the movements in the UK's financial market and 18.7% of Japan's forecast error variance, while remaining largely insulated from feedback. The findings of this study suggest that international markets are characterized by hierarchical endogeneity, challenging notions of symmetric interdependence and highlighting significant implications for financial stability frameworks making a noteworthy contribution.

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.