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Volatility Models

Fin250f: Lecture 5.2 Fall 2005 Reading: Taylor, chapter 9. Volatility Models. Outline. Stochastic volatility models ARCH(1) GARCH(1,1) GARCH(p,q) GJR and volatility asymmetry. Stochastic Volatility. Stochastic Volatility. Very straightforward Difficult to estimate Extensions:

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Volatility Models

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

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

  3. Stochastic Volatility

  4. Stochastic Volatility • 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

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