1. 2/20/08Brian Jansen Co-jumps in the Oil Industry

2. Motivational Mathematics (skip) Data Information Graphing prices Motivation for my research –Correlation in stock prices –Correlation in jumps 11/21/2006 Example Regression on Z-stats CVX –OLS –Probit Oil Intro Co-Jumps in OilBrian Jansen Outline

3. - r t,j is log return, M is total # of observations per day Realized Variance Realized Bi-Power Variation Motivational MathsBrian Jansen Realized and Bi-Power Variation

4. Motivational MathsBrian Jansen Asymptotic Properties of RV and BV

5. Motivational MathsBrian Jansen Tri-power, Max Verison BN-S

6. Sampled at the 5-minute frequency Sampled from 9/3/2002 to 1/24/2008 for 1343 total observed days Oil futures data at the 5-min frequency, from 1987 –Changing observations per day Ticker Symbols –XOM—Exxon Mobile –CVX—Chevron Oil –COP—Conoco Phillips Co-Jumps in OilBrian Jansen Data Used

7. RV, Ztp Statistics SummaryBrian Jansen Statistics Summary VariableMeanMinMax COP RV.2185(ann. vol.)1.8591e-05 0.0015 Ztp.4849-3.3579.4655 XOM RV.1935(ann. vol.)1.409e-05.0014 Ztp.4494-2.77964.7739 CVX RV.1982(ann. Vol.)1.5489e-05.0016 Ztp.4682-3.0019.9190

8. Jump AnalysisBrian Jansen Z-test Graphs XOM:29CVX:41COP:38

9. Motivational GraphsBrian Jansen XOM, CVX, COP

10. Motivational GraphsBrian Jansen XOM, CVX, COP (close up!)

11. MotivationBrian Jansen Stock Price/Jump Correlation P t COP P t XOM.97081 P t CVX.9647.9921 -Correlation between 5-minute prices -CVX had 41 jumps out of 1343 days observed; 4 of which were shared by either XOM or COP -XOM had 29 jumps out of 1343 days observed; 6 of which were shared by either CVX or COP -COP had 38 jumps out of 1343 days observed; 6 of which were shared by either CVX or XOM

12. Jump AnalysisBrian Jansen Interesting Co-Jump Days -1/13/2003: XOM and CVX -8/12/2003: CVX and COP -9/23/2003: CVX and COP -3/1/2004: XOM and COP -3/5/2004: XOM and CVX -9/14/2004: CVX and COP -9/20/2004: XOM and COP From 9/2/2004 to 9/29/2004: 1 XOM jump, 4 CVX jumps, 3 COP jumps -11/21/2006: XOM and COP, with CVX on 11/22/2006 -From 10/4/2004 to 10/29/2004: 3 XOM jumps, 2 CVX jumps, 2 COP jumps (none on the same day)

13. Jump AnalysisBrian Jansen 11/21/2006 -XOM and COP experience price jumps on Tuesday 11/21, with CVX jumping on Wednesday 11/22 -Possible reasons: -On Tuesday, Trans-Alaska pipeline slowed to 25% of normal 800,000 barrel-a-day capacity due to heavy winds -Traders worried about shutdowns at XOM’s Baytown, TX refinery— America’s biggest at 500,000 barrels-a-day -Traders looking to clear up books before Thanksgiving holiday on Thursday -On Wednesday, U.S. Energy Dept releases the information that crude oil inventories swelled by 5.1 million barrels last week -Gunmen in Nigeria seized seven hostages from an Italian supply vessel outside the delta on Wednesday -Price of oil climbs nearly $1 on Tuesday and $.93 on Wednesday

14. Z-stat RegressionBrian Jansen OLS Regression on CVX OLS:Z CVX =.253207*Z XOM +.13269*Z COP +.29 +e i

15. Z-stat RegressionBrian Jansen Probit Regression with Dummy Variables -Conclusion: We cannot use the results from a Probit model using only dummy variables indicating whether or not a jump occurs.

16. Z-stat RegressionBrian Jansen Probit Regression w/o Dummy Variables Probit: Pr(Z CVX >3.09)=Φ(.096*Z COP +.16491*Z XOM – 2.05) Example: Let Z COP =mean(Z COP )~.4849, -if Z XOM increases from 0 to 1, then Pr(Z CVX >3.09) increases by ~10%

17. Oil IntroBrian Jansen Oil Futures vs. XOM

18. Using Crude Oil Futures to check for correlation, checking for co-jumps, introduce into probit model More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility Can we use the implied volatility of same industry companies and oil futures to forecast volatility using the HAR-RV-CJ model? ConclusionBrian Jansen Extensions