crude oil price volatility ana maría herrera, liang hu, daniel pastor march 22, 2013
DESCRIPTION
Previous Work Poon and Granger (2003) Gray (1996) Klaassen (2002) Marcucci (2005) 3TRANSCRIPT
Crude Oil Price Volatility
Ana María Herrera, Liang Hu, Daniel Pastor
March 22, 2013
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Why the Crude Oil Market?
• Many implications of crude oil price uncertainty on the macroeconomy.
• Higher oil prices lead to higher production costs, which have a negative effect on GDP growth.
• The Federal Reserve considers oil price volatility when setting monetary policy.
• Large movements in oil prices may cause firms to delay investments or to alter production.
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Previous Work
• Poon and Granger (2003)• Gray (1996)• Klaassen (2002)• Marcucci (2005)
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Main Focus
• Model and forecast crude oil price volatility.
• GARCH and MS-GARCH models.
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Daily Returns of Oil Prices1/2/1986 to 12/30/2011
Daily Returns
Perc
ent C
hang
e
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Data
• Monthly spot prices for West Texas Intermediate (WTI) crude oil.
• Sample period: January 2, 1986 to December 31, 2012.
• Daily returns.• Returns are characterized by mean reversion, fat-
tails, asymmetry, and volatility clustering.• Student’s t or Generalized Error Distribution
(GED) is appropriate.
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Descriptive Statistics
MeanStandardDeviation Min Max Variance Skewness Kurtosis
0.01877 2.5731 -40.6395 19.1506 6.6213 -0.7567 17.5698
Note: Descriptive statistics for WTI rates of return. The sample period is January 2, 1986 to December 31, 2012 for 6812 observations.
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GARCH Model
• Where μt is the time varying conditional mean.• α0, α1, and γ1 are all positive• α1 + γ1 < 1 • Distributions for ηt Student’s t and GED
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GARCH Conditional Variance
GARCH Conditional Variance
Date
Volatility
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MS-GARCH Model
• Both μSt and ht are subject to the hidden Markov chain St
• Transition probability matrix:
• However, estimation is intractable due to path dependence.
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Klaassen’s (2002) Solution
• Klaassen’s approach eliminates path dependence• Multi-step ahead volatility forecasts are relatively
straightforward.
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GARCH ResultsMaximum Likelihood Estimates
GARCH-N δ 0.0281 (0.0216)σ 2.5668 (0.0125)α1 0.1065 (0.0042)γ1 0.8737 (0.0055)α1 + γ1 0.9802Log(L) -11369.1015
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MS-GARCH Results
• This confirms there are two volatility states for all models.
• State two is dominant.
Table 3: Selected Maximum Likelihood Estimates of MS-GARCH Models MRS-GARCH-N MRS-GARCH-t2 MRS-GARCH-GEDσ(1) 4.4564 1.4719 0.4627 (0.3712) (0.0622) (0.0313)σ(2) 1.6242 2.5998 2.3075 (0.0122) (0.0272) (0.0318)π1 0.1464 0.2866 0.4127π2 0.8536 0.7134 0.5873α(1)
1 + γ(1)1 0.7855 0.8887 0.9674
α(2)1 + γ(2)
1 0.9812 0.9825 0.9808
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MS-GARCH ResultsTable 3: Selected Maximum Likelihood Estimates of MS-GARCH Models
MRS-GARCH-N MRS-GARCH-t2 MRS-GARCH-GEDν(1) - 6.5624 1.3579 (1.0273) (0.0266)ν(2) - 6.0386 (0.4622)
Log(L) -14520.1688 -14369.9502 -14410.1269
N. of Par. 10 12 11
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1401-Day Forecast of GARCH-N vs. Realized Volatility
GARCH-N 1 Day Forecast Realized Volatility
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1-Day Forecast of MS-GARCH-N vs. Realized Volatility
MS GARCH-N 1 Day Forecast Realized Volatility
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Evaluation of Volatility Forecasts
• Seven different loss functions used for in sample comparison of MS-GARCH models.
• MS-GARCH-t2 ranks first or second in all but one.
• A model where the degrees of freedom parameter is allowed to switch between regimes seems the best.
• Out-of-sample forecast evaluation forthcoming.
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Questions?