Volatility Models

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Volatility Models

• Fin250f Lecture 5.2
• Fall 2005
• Reading Taylor, chapter 9

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Outline

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

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Stochastic Volatility
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Stochastic Volatility

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

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ARCH(1)Autoregressive Conditional
Heteroskedasticity
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ARCH(1)

• Alphalt1
• Omegagt0
• Squared return correlations not persistent enough

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GARCH(1,1)
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GARCH(1,1) standardized residuals
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GARCH(1,1)

• Most heavily used volatility model on Wall St.
• Estimation
• maximum likelihood (not too difficult)
• Moments
• Variance
• Skew 0
• Kurtosis gt 3

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GARCH volatility forecasts
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More volatility forecasts