GARCH (1,1) Model
We will cover following topics
Introduction
The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is a powerful tool used to estimate and forecast volatility in financial markets. Developed by Robert F. Engle in the 1980s, the GARCH (1,1) model accounts for the clustering of volatility observed in financial time series data. In this chapter, we delve into the mechanics of the GARCH (1,1) model, its components, and how it can be applied to estimate volatility for risk assessment and prediction.
Components of the GARCH Model
The GARCH
1) Autoregressive Component (AR): The autoregressive component captures the persistence of volatility shocks. It accounts for the fact that recent volatility shocks tend to influence future volatility. Mathematically, the AR component can be represented as:
Where:
is the conditional variance at time . is the constant term. is the coefficient of the autoregressive term. is the squared residual at time . is the coefficient of the moving average of squared shocks term. is the conditional variance at time .
2) Moving Average Component (MA): The moving average component accounts for the persistence of past squared shocks. It reflects the idea that past volatility shocks continue to impact future volatility. The MA component can be viewed as a form of volatility persistence.
Applying the GARCH Model
To apply the GARCH
2) Choose an appropriate lag length: Determine the number of lagged terms to include in the model.
3) Estimate the model parameters: Use optimization techniques to estimate the values of
4) Evaluate model diagnostics: Check for model adequacy and assess the goodness-of-fit.
5) Forecast future volatility: Use the estimated GARCH
Example: Suppose you have daily stock price returns data for a specific asset. By applying the GARCH
Conclusion
The GARCH (1,1) model offers a robust framework for estimating volatility in financial markets. By considering both past squared shocks and past conditional variances, the model captures volatility clustering and persistence. This chapter has provided insights into the model’s components, application steps, and its role in enhancing risk assessment and prediction. GARCH modeling equips financial professionals with a valuable tool for understanding and managing volatility, a cornerstone of modern finance.