Final Presentation: Jump statistics and volume Econ 201 FS April 22, 2009 Pat Amatyakul

Last time Regressed jump statistics on daily volume for the BNS test, Jiang-Oomen test, and Ait- Sahalia Jacod test. Note that for the stocks where the value is statistically significant, BNS and Ait-Sahalia test yields a positive relationship while Jiang Oomen yiled a negative relationship

This time Plotted out the Jiang-Oomen test statistic to see why the relationship is different Revise coding Regress volume on the jump statistics, as well as the lag of volume

Volume vs. Day of the week revisited JNJ KO PG T

Jiang Oomen swap variance ratio jump test The assumption here is that the swap variance should equal the realized variance if no jumps are detected Swap variance is defined as: The test statistic is

One sample plot of the test statistic

Jump detection This is a two-sided jump test. These are the percentage of jumps detected at the 95% confidence level Jump days JNJ28.4%CSCO26.4% JPM26.9%GE23.8% PG25.2%IBM28.7% KO24.8%MSFT26.0% T29.1%PFE27.4%

Redoing the simple jiang regression Regressing the absolute value of the jiang statistics on volume coefficientp-value coefficientp-value JNJ-3.06E CSCO-2.65E JPM-9.43E GE-1.86E PG-3.10E IBM4.28E KO-3.78E MSFT-1.21E T-2.67E PFE-5.66E

Rethinking the regression Volume clustering tend to occur, that is, volume today tend to affect volume tomorrow so I included a few lag volume terms into the regressors Volume on Monday seemed to be lower than every other day of the week, so I included that into my regressors Made some minor adjustment from last time to make sure that the signs of the coefficient means the same thing in all of the three jump statistics

The regression The regression is as follows Where the stat is either the BNS z-stat, the absolute value of the Jiang-Oomen z-stat, and  -ASJ variable for the Ait-Sahalia Jacod test Monday is a 0 or 1 dummy variable

stat Volume (t-1) Volume (t-5)Mondaycons JNJBNS coef p-value JO coef p-value ASJ coef p-value0.000 JPMBNS coef p-value JO coef p-value ASJ coef p-value

stat Volume (t-1) Volume (t-5)Mondaycons PGBNS coef p-value JO coef p-value ASJ coef p-value0.000 KOBNS coef p-value JO coef p-value ASJ coef p-value0.000

stat Volume (t-1) Volume (t-5)Mondaycons TBNS coef p-value JO coef p-value ASJ coef p-value CSCOBNS coef E+07 p-value JO coef E+07 p-value ASJ coef E+07 p-value

stat Volume (t-1) Volume (t-5)Mondaycons GEBNS coef p-value JO coef p-value ASJ coef p-value IBMBNS coef E+06 p-value JO coef E+06 p-value0.000 ASJ coef E+06 p-value0.000

stat Volume (t-1) Volume (t-5)Mondaycons MSFTBNS coef E+07 p-value JO coef E+07 p-value ASJ coef E+07 p-value PFEBNS coef E+06 p-value JO coef E+06 p-value ASJ coef E+06 p-value

Summary of results The correlation between volume and its lag term seems quite high and significant BNS test does not yield any conclusive results, only 2/10 are significant and it is a split between a positive correlation and negative correlation For the JO test, 5/10 are significant and 4 showed a negative relationship and 1 showed a positive relationship. For the Ait-Sahalia Jacod test, 9/10 are significant and all showed a negative relationship between volume and jump statistics

Interpretation According to Tauchen and Pitts (1983), changes in prices and volume are related Need to investigate how this is related to each test statistics, since the change in prices provide the basis for calculating all the test statistics

Applications In general, at least for JO and ASJ tests, lower volume corresponds with higher chance of jump days Since volume is an easy indicator to observe in the market, one could flag an especially low volume day to possibly correspond with a jump. This would work only for the ASJ test, because it seems like the coefficient in the JO test regression are rather small. Might be able to somehow incorporate this into asset pricing