Search Results (6)

This paper compares the daily return volatility by four leading international indices: JSE Top 40, FTSE 100, Nikkei 225 and S&P/ASX 200. The return series are modelled in ARMA process, where ARMA(1,3) values are taken for JSE Top 40 and S&P/ASX 200, ARMA(0,0) for FTSE 100, and ARMA(1,2) for Nikkei 225. The volatility is modelled in APARCH and GJR-GARCH (e.g., under various conditional distributions including Student-t (STD), skewed Student-t (SSTD), generalised error distribution (GED), skewed generalised error distribution (SGED), and generalised hyperbolic distribution (GHYD)). Model selection results based on information criteria indicate that the APARCH models outperform their GJR-GARCH counterparts in all cases. In particular, the ARMA(p,q)-APARCH(1,1) with SSTD is most suitable for the JSE Top 40 and the FTSE 100. The model that best describes the Nikkei 225 is an ARMA(1,2)–APARCH(1,1) model with SGED, and the S&P/ASX 200 fits an ARMA(1,3)-APARCH(1,1) model with GHYP. Among the indices, the FTSE 100 has the highest volatility persistence, while the Nikkei 225 responds more quickly to shocks. This out-of-sample forecasting test shows that ARMA(p,q)-APARCH(p,q) provides more accurate volatility predictions, especially for JSE Top 40 and S&P/ASX 200 investors. Full article

This study investigates the volatility dynamics of the Bahrain All Share Index (BAX) between 2010 and 2025, a period marked by COVID-19 and regional geopolitical shocks. Using ARMA (1,1) to model returns and four GARCH-family models (ARCH, GARCH, EGARCH, GJR-GARCH) to capture volatility, we provide new evidence from a bank-based frontier market that has received limited empirical attention. The results reveal that returns are stationary and exhibit volatility clustering. Among the competing models, EGARCH (1,1) provides the best fit—exhibiting the lowest AIC and SIC values and the highest log-likelihood—revealing a significant leverage effect whereby negative shocks generate stronger volatility than positive shocks. This asymmetric volatility pattern contradicts earlier findings for Bahrain but aligns with theoretical expectations for bank-based financial systems. The findings carry implications for investors in terms of portfolio risk management, derivative pricing, and asset allocation. They also have important implications for regulators and policymakers, suggesting that counter-cyclical buffers and interest rate adjustments could be applied to stabilize the market in anticipation of negative shocks. These insights enrich the scarce literature on volatility in small frontier markets and contribute to a more nuanced understanding of the volatility dynamics in the MENA region. Full article

This study develops an integrated risk modeling framework to assess capital adequacy and optimize portfolio performance for Thai life and non-life insurers. Leveraging ARMA–GJR–GARCH models with skewed Student-t innovations, extreme value theory, and dynamic R-vine copulas, the framework effectively captures volatility, tail risks, and evolving asset interdependencies. Utilizing daily data from 2014 to 2024, the models generate value-at-risk forecasts consistent with international standards such as Basel III’s 10-day 99% VaR and rolling Sharpe ratios for portfolios integrating green bonds compared to traditional asset allocations. The results demonstrate that green bonds, fixedincome instruments funding renewable energy and other environmental projects, significantly improve risk-adjusted returns and have the potential to reduce capital requirements, particularly for life insurers with long-term sustainability mandates. These findings underscore the importance of portfolio-level capital assessment and support the proactive integration of ESG considerations into supervisory investment guidelines to enhance financial resilience and align the insurance sector with Thailand’s sustainable finance agenda. Full article

Volatility modelling is a key feature of financial risk management, portfolio optimisation, and forecasting, particularly for market indices such as the JSE Top40 Index, which serves as a benchmark for the South African stock market. This study investigates volatility modelling of the JSE Top40 Index log-returns from 2011 to 2025 using a hybrid approach that integrates statistical and machine learning techniques through a two-step approach. The ARMA(3,2) model was chosen as the optimal mean model, using the auto.arima() function from the forecast package in R (version 4.4.0). Several alternative variants of GARCH models, including sGARCH(1,1), GJR-GARCH(1,1), and EGARCH(1,1), were fitted under various conditional error distributions (i.e., STD, SSTD, GED, SGED, and GHD). The choice of the model was based on AIC, BIC, HQIC, and LL evaluation criteria, and ARMA(3,2)-EGARCH(1,1) was the best model according to the lowest evaluation criteria. Residual diagnostic results indicated that the model adequately captured autocorrelation, conditional heteroskedasticity, and asymmetry in JSE Top40 log-returns. Volatility persistence was also detected, confirming the persistence attributes of financial volatility. Thereafter, the ARMA(3,2)-EGARCH(1,1) model was coupled with XGBoost using standardised residuals extracted from ARMA(3,2)-EGARCH(1,1) as lagged features. The data was split into training (60%), testing (20%), and calibration (20%) sets. Based on the lowest values of forecast accuracy measures (i.e., MASE, RMSE, MAE, MAPE, and sMAPE), along with prediction intervals and their evaluation metrics (i.e., PICP, PINAW, PICAW, and PINAD), the hybrid model captured residual nonlinearities left by the standalone ARMA(3,2)-EGARCH(1,1) and demonstrated improved forecasting accuracy. The hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model outperforms the standalone ARMA(3,2)-EGARCH(1,1) model across all forecast accuracy measures. This highlights the robustness and suitability of the hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost model for financial risk management in emerging markets and signifies the strengths of integrating statistical and machine learning methods in financial time series modelling. Full article

This paper investigates five different Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Condition-al Heteroscedacity (GARCH models (GARCH, exponential GARCH or EGARCH, integrated GARCH or IGARCH, Component GARCH or CGARCH and the Glosten-Jagannathan-Runkle GARCH or GJR-GARCH) along with six distributions (normal, Student’s t, GED and their skewed forms), which are used to estimate the price dynamics of the Bulgarian stock index SOFIX. We use the best model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data cover the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at analysing the SOFIX price and which distribution is most appropriate. The results, based on the BIC and AIC, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student’s t-distribution is preferred for modelling. From the results obtained, we can confirm that the CGARCH model specification supports a more appropriate description of SOFIX volatility than a simple GARCH model. We find that long-term shocks have a more persistent impact on volatility than the effect of short-term shocks. Furthermore, for the same magnitude, negative shocks to SOFIX prices have a more significant impact on volatility than positive shocks. According to the results, when predicting future values of SOFIX, it is necessary to include both a first-order autoregressive component and a first-order moving average in the mean equation. With the help of 5000 simulations, it is estimated that the chances of SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087. Full article

Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks’ asymmetric return volatility and investors’ risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors’ risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia’s capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible. Full article