Visualize how volatility clusters in financial time series using the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model.
About GARCH Models
The GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model is widely used in finance to model and forecast volatility. It captures the "volatility clustering" phenomenon where large changes tend to be followed by large changes (of either sign) and small changes tend to be followed by small changes.
The GARCH(1,1) model is defined by:
σt2 = ω + αεt-12 + βσt-12
Where:
- σt2: Conditional variance (volatility) at time t
- ω: Long-run average variance
- α: Weight given to previous period's squared shock (ARCH term)
- β: Weight given to previous period's variance (GARCH term)
- εt-1: Shock (return) at time t-1
Key properties of GARCH models:
- They capture volatility clustering seen in financial markets
- The sum of α + β determines volatility persistence (closer to 1 means more persistent)
- Widely used in options pricing and risk management (VaR calculations)
- Forms the basis for more complex models like EGARCH and GJR-GARCH