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

2. Motivational Mathematics (skip) Data Information (skip) Graphing prices Motivation for my research –Correlation in stock prices –Correlation in returns Factor Analysis –Z-stats –RV –RV-BV Extensions 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 12/31/07 for 1323 total observed days Oil futures data at the 5-min frequency, from 1987 –Changing number of observations per day –Different trading days than equity stocks 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. GraphsBrian Jansen Stock Returns

13. GraphsBrian Jansen Stock Returns (Zoom)

14. StatisticsBrian Jansen Stock Returns R t COP R t CVX.9741 R t XOM.857.843 -High degree of correlation between the stock returns, especially between CVX and COP

15. GraphsBrian Jansen Oil Futures vs. XOM Prices

16. GraphsBrian Jansen Oil Futures vs. COP Returns

17. StatisticsBrian Jansen Stock Returns RtCOPRtCVXRtXOMRtOIL RtCOP1 RtCVX.9741 RtXOM.857.8431 RtOIL.341.322.2221 -Not great correlation between any of the stocks and oil returns -Questionable return for oil given the nature of the data

18. Factor AnalysisBrian Jansen Z-Statistic Analysis -For both COP and CVX, Factor1 is loads positively and most variance is explained by common factors (high communality)

19. Factor AnalysisBrian Jansen Z-Statistic Analysis w/ PCF -Principle-Component Factors: treating the communalities (1-uniqueness) as 1, thus allowing for no unique factors

20. Interesting: With RV, we see Factor1 explaining COP and XOM, with a high degree of communality Factor AnalysisBrian Jansen RV Analysis

21. Factor AnalysisBrian Jansen RV Analysis w/ PCF -When communality is forced to be 1, Factor1 explains COP and XOM while Factor 2 explains CVX and OIL

22. Pretty terrible results for RV-BV Factor AnalysisBrian Jansen RV-BV Analysis

23. More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility Introducing a new jump test that can detect multiple jumps per day and time of jump. Lee-Mykland (2008)? Dobrev et. al (2007) Auto correlation with small lag times 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