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Abstract

This study examines methodological developments in modeling financial market volatility, with a particular focus on Bayesian nonparametric approaches as flexible alternatives to traditional parametric models such as GARCH and stochastic volatility frameworks. While characteristics of financial time series—including fat tails, volatility clustering, asymmetry, and structural breaks—limit the effectiveness of rigid parametric specifications, nonparametric Bayesian tools such as Dirichlet Process Mixtures offer adaptive probabilistic structures that better capture the true behavior of returns.
Using daily data from the ISX Main 60 Index, the empirical analysis shows that although the GARCH(1,1) model achieves a good statistical fit, stable volatility estimates, and accurate short-term risk evaluation, it remains insufficient in modeling tail deviations and asymmetric responses to market shocks. In contrast, the DPMM and BNP models demonstrate stronger flexibility and significantly superior performance, with DPMM achieving the lowest error metrics and offering a more realistic representation of the distributional and dynamic properties of returns. These findings highlight the importance of adopting Bayesian nonparametric methods for improved forecasting accuracy and more robust volatility modeling in emerging and structurally volatile markets.

Keywords

Bayesian nonparametric modeling, Dirichlet mixture, Gaussian processes, GARCH model, Financial forecasting

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