1. Volatility Models Fin250f: Lecture 5.2 Fall 2005 Reading: Taylor, chapter 9

2. Outline  Stochastic volatility models  ARCH(1)  GARCH(1,1)  GARCH(p,q)  GJR and volatility asymmetry

3. Stochastic Volatility

4.  Very straightforward  Difficult to estimate  Extensions: h(t) follows discrete markov process

5. ARCH(1) Autoregressive Conditional Heteroskedasticity

6. ARCH(1)  Alpha<1  Omega>0  Squared return correlations not persistent enough

7. GARCH(1,1)

8. GARCH(1,1) standardized residuals

9. GARCH(1,1)  Most heavily used volatility model on Wall St.  Estimation: maximum likelihood (not too difficult)  Moments Variance Skew = 0 Kurtosis > 3

10. GARCH volatility forecasts

11. More volatility forecasts