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Forecasting 2001 - ARCH models

Forecasting 2001 - ARCH models - Forecasting Financial...

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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 1 Forecasting Financial Markets ARCH Models Copyright © 1999-2006 Investment Analytics
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 2 Overview ¾ Asset Return Behavior ¾ Models 9 ARCH 9 GARCH 9 GARCH-M ¾ Estimation procedures ¾ Applications
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 3 Defining Volatility ¾ Nonparametric Definition 9 X is more volatile than y if: 9 P(|X|>c) > P(|Y|>c) for all c ¾ Time Series Volatility 9 Time series y t become more volatile when P(| y t+1 | >c) > P(| y t | > c) for all c Occurs if and only if σ t=1 > σ t
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 4 Estimating Historical Volatility ¾ Standard Deviation ¾ Parkinson (5x times more efficient) ¾ Garman & Klass (7 x efficiency) ) 1 /( ) ( ) / ( 2 1 = = + N X X P P Ln X i i i i σ ) / ( ) 2 ( 2 1 i i L H Ln Ln N = σ= ABS N Ln H L N Ln Ln C C ii [[ ( / ) ] (( ) ) [ ( / ) ] ] 11 2 1 22 1 2 1 2
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 5 Asset Return Characteristics ¾ Thick Tails ¾ Non-Normal Distribution ¾ Volatility Clustering ¾ Leverage ¾ Trading vs. Non Trading Periods ¾ Forecastable Events ¾ Volatility & Correlation
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 6 Thick Tails, Non-Normal Distribution 9 Mandelbrot (1963), Fama (1963, 1965) Normal(0.007, 0.041) X <= 0.075 95.0% X <= -0.061 5.0% 0 2 4 6 8 10 12 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 S&P500 Index Monthly Returns 1/1950-2/2001 Skewness = -0.6 Kurtosis = 5.7
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 7 Volatility is Stochastic ¾ Non-Constant Variance 9 Changing conditional variance 9 Highly volatile periods 9 Interspersed with quiet periods 9 Large returns tend to be followed by large returns (positive or negative)
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 8 A Conditionally Heteroscedastic Series -6% -4% -2% 0% 2% 4% 6% 8% 10%
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 9 Volatility Clustering 9 Periods of high vol. followed by high vol. 9 Followed by decay back to normal levels SP500 Index Volatility 0% 20% 40% 60% 80% 100% 120% 140% 160% Jan-50 Jan-52 Jan-54 Jan-56 Jan-58 Jan-60 Jan-62 Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 10 Volatility Distributions LogLogistic(-5, 2.8, 12.4) X <= -1.4954 95.0% X <= -2.8176 5.0% 0 0.2 0.4 0.6 0.8 1 1.2 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 Enron: Volatility Distribution 9/83 - 2/01
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 11 The Volatility Cone V o l at i t y ( % ) Days 03 0 60 Maximum Minimum A v e r a g
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Copyright © 1999-2006 Investment Analytics Forecasting Financial Markets – ARCH Models Slide: 12 Leverage Effect ¾ Black (1976) 9
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Forecasting 2001 - ARCH models - Forecasting Financial...

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