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

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

- 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

Motivational MathsBrian Jansen Asymptotic Properties of RV and BV

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

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

RV, Ztp Statistics SummaryBrian Jansen Statistics Summary VariableMeanMinMax COP RV.2185(ann. vol.)1.8591e Ztp XOM RV.1935(ann. vol.)1.409e Ztp CVX RV.1982(ann. Vol.)1.5489e Ztp

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

Motivational GraphsBrian Jansen XOM, CVX, COP

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

MotivationBrian Jansen Stock Price/Jump Correlation P t COP P t XOM P t CVX 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

GraphsBrian Jansen Stock Returns

GraphsBrian Jansen Stock Returns (Zoom)

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

GraphsBrian Jansen Oil Futures vs. XOM Prices

GraphsBrian Jansen Oil Futures vs. COP Returns

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

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)

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

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

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

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

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