In this paper, we propose a new generalization of the log-t distribution using the Kumaraswamy distribution, aiming to better characterize the behavior of financial stock prices. The objective is to model the dynamic relationship between stock prices and trading volumes in Gulf Cooperation Council (GCC) economies, compare the model’s performance against traditional distributions, and evaluate financial risks using Value at Risk (VaR) and Expected Shortfall (ES). The fitting of distributions to the data is achieved through maximum likelihood estimation. Our analysis reveals that the proposed model surpasses other distributional models, including \(\log -t\) and lognormal distributions, in explaining the observed data sets. To assess goodness of fit, we employ three information criteria and likelihood ratio tests. We also examine the extremes of these stock indices using the Generalized Extreme Value (GEV) distribution, from which estimates of VaR and ES are derived. The results show that DFMGI and ADSMI exhibit the lowest VaR and ES estimates, indicating lower risk exposure, while BHSEASI displays the highest risk levels. This finding underscores the ability of our model to effectively differentiate risk profiles across diverse markets. The proposed distribution offers a significant contribution to the literature by providing a robust framework for accurately assessing tail risks, making it a valuable tool for financial risk managers. Finally, we analyze the extreme dependencies between Islamic stock indices (specifically the Dow Jones Islamic Market GCC Index - DJIMGCC) and conventional stock indices of the GCC countries using extreme correlation plots. These correlation plots can help investors identify indices that may offer diversification benefits by highlighting which indices to include or exclude based on their extreme dependence structure with the conventional (DJIMGCC) markets, especially during financial crises.
