motivational mathematics (skip) data information graphing prices motivation for my research
DESCRIPTION
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. - r t,j is log return, M is total # of observations per day. - PowerPoint PPT PresentationTRANSCRIPT
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