2/20/08 Brian Jansen

Co-jumps in the Oil Industry

• 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 Oil Brian Jansen

Outline

-rt,j is log return, M is total # of observations per day

• Realized Variance

• Realized Bi-Power Variation

Motivational Maths Brian Jansen

Realized and Bi-Power Variation

Motivational Maths Brian Jansen

Asymptotic Properties of RV and BV

Motivational Maths Brian Jansen

Tri-power, Max Verison BN-S

• 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 Oil Brian Jansen

Data Used

RV, Ztp Statistics Summary Brian Jansen

Statistics Summary

Variable Mean Min Max

COP

RV .2185(ann. vol.) 1.8591e-05 0.0015

Ztp .4849 -3.357 9.4655

XOM

RV .1935(ann. vol.) 1.409e-05 .0014

Ztp .4494 -2.7796 4.7739

CVX

RV .1982(ann. Vol.) 1.5489e-05 .0016

Ztp .4682 -3.001 9.9190

Jump Analysis Brian Jansen

Z-test Graphs

XOM:29 CVX:41 COP:38

Motivational Graphs Brian Jansen

XOM, CVX, COP

Motivational Graphs Brian Jansen

XOM, CVX, COP (close up!)

Motivation Brian Jansen

Stock Price/Jump Correlation

PtCOP PtXOM

PtXOM .9708 1PtCVX .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

Jump Analysis Brian 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)

Jump Analysis Brian 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

Z-stat Regression Brian Jansen

OLS Regression on CVX

_cons .2900586 .0379297 7.65 0.000 .2156505 .3644666 z_cop .1326957 .0256406 5.18 0.000 .0823956 .1829958 z_xom .253207 .0282472 8.96 0.000 .1977934 .3086205 z_cvx Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 2250.97967 1342 1.67733209 Root MSE = 1.2433 Adj R-squared = 0.0785 Residual 2071.2509 1340 1.54570962 R-squared = 0.0798 Model 179.728772 2 89.864386 Prob > F = 0.0000 F( 2, 1340) = 58.14 Source SS df MS Number of obs = 1343

. reg z_cvx z_xom z_cop, he

z_xom 0.0887 0.2479 1.0000 z_cvx 0.1571 1.0000 z_cop 1.0000 z_cop z_cvx z_xom

(obs=1343). cor z_cop z_cvx z_xom

OLS: ZCVX=.253207*ZXOM + .13269*ZCOP + .29 +ei

Z-stat Regression Brian Jansen

Probit Regression with Dummy Variables

_cons -1.893199 .0706502 -26.80 0.000 -2.031671 -1.754727 iz_cop .231805 .3452664 0.67 0.502 -.4449047 .9085148 iz_xom .3794999 .3621439 1.05 0.295 -.3302891 1.089289 iz_cvx Coef. Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -182.65642 Pseudo R2 = 0.0042 Prob > chi2 = 0.4658 LR chi2(2) = 1.53Probit regression Number of obs = 1343

-Conclusion: We cannot use the results from a Probit model using only dummy variables indicating whether or not a jump occurs.

Z-stat Regression Brian Jansen

Probit Regression w/o Dummy Variables

Probit: Pr(ZCVX>3.09)=Φ(.096*ZCOP + .16491*ZXOM – 2.05)

Example: Let ZCOP=mean(ZCOP)~.4849,

-if ZXOM increases from 0 to 1, then Pr(ZCVX>3.09) increases by ~10%

_cons -2.052478 .0910043 -22.55 0.000 -2.230843 -1.874113 z_xom .1649142 .0563325 2.93 0.003 .0545046 .2753238 z_cop .0967888 .0481275 2.01 0.044 .0024606 .191117 iz_cvx Coef. Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -176.45514 Pseudo R2 = 0.0380 Prob > chi2 = 0.0009 LR chi2(2) = 13.93Probit regression Number of obs = 1343

Oil Intro Brian Jansen

Oil Futures vs. XOM

• 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?

Conclusion Brian Jansen

Extensions