<![CDATA[This study investigates the financial volatility of the SPDR S&P 500 ETF (SPY) using two distinct approaches the Rolling Window Volatility (20-day) and the GARCH (1,1) Approximation to analyze and compare the dynamic behavior of market risk. The analysis utilizes daily SPY price data to compute logarithmic returns and model volatility persistence over time. Descriptive statistics indicate that SPY returns exhibit volatility clustering, leptokurtosis, and negative skewness, implying that extreme market movements occur more frequently than predicted by a normal distribution. Empirical results show that both volatility measures successfully capture the cyclical nature of market risk but differ in responsiveness and interpretability. The rolling window method provides an intuitive and historical view of volatility patterns, while the GARCH (1,1) model captures conditional and time-varying volatility more effectively by incorporating both short-term shocks and long-term persistence. Comparative analysis reveals that GARCH estimates produce smoother and more adaptive volatility dynamics, making them more suitable for forecasting and real-time risk assessment. Overall, the findings confirm that volatility in financial markets is not constant but evolves dynamically in response to new information and investor behavior. The study emphasizes the importance of conditional volatility models in improving the accuracy of risk evaluation, portfolio management, and market forecasting, particularly during periods of heightened uncertainty.]]>
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