Motivational Mathematics (skip)

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2/20/08 Brian Jansen
Co-jumps in the Oil Industry Co-jumps in the Oil Industry Co-jumps in the Oil Industry
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Co-Jumps in Oil Brian Jansen
Outline Outline Outline

• 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

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-rt,j is log return, M is total of observations
per day
Motivational Maths Brian Jansen
Realized and Bi-Power Variation Realized and Bi-Power Variation Realized and Bi-Power Variation

• Realized Variance
• Realized Bi-Power Variation

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Motivational Maths Brian Jansen
Asymptotic Properties of RV and BV Asymptotic Properties of RV and BV Asymptotic Properties of RV and BV
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Motivational Maths Brian Jansen
Tri-power, Max Verison BN-S Tri-power, Max Verison BN-S Tri-power, Max Verison BN-S
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Co-Jumps in Oil Brian Jansen
Data Used Data Used Data Used

• 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
• XOMExxon Mobile
• CVXChevron Oil
• COPConoco Phillips

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RV, Ztp Statistics Summary Brian Jansen
Statistics Summary Statistics Summary Statistics Summary
Variable Mean Min Max
COP RV .2185(ann. vol.) 1.8591e-05 0.0015
COP Ztp .4849 -3.357 9.4655
XOM RV .1935(ann. vol.) 1.409e-05 .0014
XOM Ztp .4494 -2.7796 4.7739
CVX RV .1982(ann. Vol.) 1.5489e-05 .0016
CVX Ztp .4682 -3.001 9.9190
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Jump Analysis Brian Jansen
Z-test Graphs Z-test Graphs Z-test Graphs
XOM29
CVX41
COP38
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Motivational Graphs Brian Jansen
XOM, CVX, COP XOM, CVX, COP XOM, CVX, COP
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Motivational Graphs Brian Jansen
XOM, CVX, COP (close up!) XOM, CVX, COP (close up!) XOM, CVX, COP (close up!)
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Motivation Brian Jansen
Stock Price/Jump Correlation Stock Price/Jump Correlation Stock Price/Jump Correlation
-Correlation between 5-minute prices
PtCOP PtXOM
PtXOM .9708 1
PtCVX .9647 .9921
-XOM had 29 jumps out of 1343 days observed 6 of
which were shared by either CVX or COP
-CVX had 41 jumps out of 1343 days observed 4 of
which were shared by either XOM or COP
-COP had 38 jumps out of 1343 days observed 6 of
which were shared by either CVX or XOM
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Jump Analysis Brian Jansen
Interesting Co-Jump Days Interesting Co-Jump Days 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)
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Jump Analysis Brian Jansen
11/21/2006 11/21/2006 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 XOMs
Baytown, TX refinery Americas 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
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Z-stat Regression Brian Jansen
OLS Regression on CVX OLS Regression on CVX OLS Regression on CVX
OLS ZCVX.253207ZXOM .13269ZCOP .29 ei
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Z-stat Regression Brian Jansen
Probit Regression with Dummy Variables Probit Regression with Dummy Variables 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.
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Z-stat Regression Brian Jansen
Probit Regression w/o Dummy Variables Probit Regression w/o Dummy Variables Probit Regression w/o Dummy Variables
Probit Pr(ZCVXgt3.09)F(.096ZCOP .16491ZXOM
2.05) Example Let ZCOPmean(ZCOP).4849, -if
ZXOM increases from 0 to 1, then Pr(ZCVXgt3.09)
increases by 10
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Oil Intro Brian Jansen
Oil Futures vs. XOM Oil Futures vs. XOM Oil Futures vs. XOM
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Conclusion Brian Jansen
Extensions Extensions Extensions

• 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?