Volatility

							Introduction to Volatility
Models

    From Ruey. S. Tsay’s slides
Characteristics of Volatility
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
Structure of Volatility Models
Basic idea: Shocks of asset returns are NOT serially
correlated, but dependent.
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.
ARCH Model
ARCH Model Properties
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
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.
GARCH Model
ARCH Model Properties