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

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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

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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?