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
Vola
tility
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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?
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