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

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Presentation transcript:

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

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

Stochastic Volatility

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

ARCH(1) Autoregressive Conditional Heteroskedasticity

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

GARCH(1,1)

GARCH(1,1) standardized residuals

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

GARCH volatility forecasts

More volatility forecasts