Introduction to Volatility Models

1
Introduction to Volatility Models

• From Ruey. S. Tsays slides

2
Characteristics of Volatility
3
Characteristics of Volatility

• Not directly observable
• Existence of volatility clusters (volatility
  maybe high for certain time periods and low for
  other periods)
• Evolving over time in a continuous manner
• Volatility does not diverge to infinity, i.e.
  volatility is stationary
• Volatility reacts differently to big price
  increase/drop

4
Structure of Volatility Models
Basic idea Shocks of asset returns are NOT
serially correlated, but dependent.
5
Model Building Steps

• Specify a mean equation by testing for serial
  dependence in the data.
• Use the residuals of the mean equation to test
  for ARCH effects.
• Specify a volatility model if ARCH effects are
  statistically significant and perform a joint
  estimation of the mean and volatility equation.
• Check the fitted model and refine it if necessary.

6
ARCH Model
7
ARCH Model Properties
8
Pro and Con of ARCH Model

• Pro
• Simplicity
• Generates Volatility Clustering
• Heavy Tails (outlier study)
• Con
• Symmetric btw positive negative prior returns
• Restrictive
• Provides no explanation
• Not sufficiently adaptive in prediction

9
Building an ARCH Model

• Modeling the mean effect and testing
• Use Q-statistics of squared residuals McLeod and
  Li (1983) Engle (1982)
• Order determination
• Use PACF of the squared residuals
• Estimation
• Conditional MLE
• Model checking
• Q-stat of standardized residuals and squared
  standardized residuals. Skewness Kurtosis of
  standardized residuals.

10
GARCH Model
11
ARCH Model Properties