Volatility Analysis of Returns of Financial Assets Using a Bayesian Time-Varying Realized GARCH-Itô Model

In a stage of more and more complex and high-frequency financial markets, the volatility analysis is a cornerstone of modern financial econometrics with practical applications in portfolio optimization, derivative pricing and systematic risk assessment. This paper introduces a novel Bayesian Time-varying Generalized Autoregressive Conditional Heteroskedasticity (BtvGARCH-Itô) model designed to improve the precision and flexibility of volatility modeling in financial markets. Original GARCH-Itô models, while effective in capturing realized volatility and intraday patterns, rely on fixed or constant parameters thus it is limited to study structural changes. Our proposed model addresses this restraint by integrating the continuous-time Ito process with time-varying Bayesian inference to allow parameters to vary over time based on prior beliefs to quantify uncertainty and minimize overfitting especially in small-sample or high-dimensional settings. Through simulation studies using sample sizes of N=100 and N=200, we find that BtvGARCH-Itô outperformed original GARCH-Itô in-sample fit and out-of-sample forecast accuracy based on posterior estimates comparison with true parameter values and forecasting error metrics. For the empirical validation, this model is applied to analyze volatility of S&P500 and Bitcoin (BTC) using one minute length data for S&P500 (from 2023-01-03 to 2024-12-31) and BTC (from 2023-01-01 to 2025-01-01). This model has a potential as a robust tool and new direction in volatility modeling for financial risk management.