1. Comparison of Lee-Mykland and BNS Statistics
March 28, 2007
Warren Davis

2. Outline Partial Review of Previous Research
Overview of Lee-Mykland Jump Test
Discussion of Results of Lee-Mykland
Future Research Directions

3. Davis 3
Mathematical Methods
Using the following differential equation for log-price p(t),
And the following definition of the jth return on day t with M returns per day,
Returns were examined at 5-minute intervals, or every ten readings

4. Measures of Integrated Volatility
Davis 4
Measures of Integrated Volatility

5. Davis 5
Z-Statistics Test
To flag jump days, a z-statistic was computed using both the Tri-Power Quarticity and Quad-Power Quarticity as follows:

6. Davis 6
Flagged Days: 48

7. Flagged Jump Days

8. Key Events Four Primary Events on Jump Days
FDA Approvals, Drug News (26)
Lawsuits and Investigations for and against BMS (8)
Accounting Scandals, Results Statements,etc. (17)
Selling or Buying of Company Units (18)
There are several minor causes, such as CEO appointments, one interest rate announcement, and five flagged days that did not yield a probable cause

10. The Pharmaceutical Industry
Pfizer and Merck were both analyzed using the same jump flagging technique.
Pfizer flagged 28 jumps
Merck flagged 35 jumps
BMS shared 2 with Pfizer
BMS shared 2 with Merck
Pfizer shared 1 with Merck
No flagged days were shared by all three

11. Lee and Mykland (2006)

12. Lee and Mykland Results
Using a .999 significance level, and the recommended window size K=268, 1507 jumps were found
Out of these, 436 days had more than one jump flagged
If window size was decreased, the number of flagged jump days rose dramatically

13. Results (cont.)
After increasing the significance level and decreasing window size, a small number of flagged jumps were analyzed and compared to BNS flagged days
Only 3 of BNS’s 48 flagged days were contained in the data

14. Results (cont.) K 5 Min 17.5 Min 3 242 90 6 990 270 10 1274 371 30
1705
407 50
1758
395 75
1564
399
100
1516
402
200
1532
393
268
1507
390
500
1500
1000
1472

16. Results (cont.) Even with 17.5 minute returns, jump days were analyzed
Still only 3 days also flagged by BNS statistics- not the same as the 3 previously found to be in common

17. Future Research Directions
Appear to be slightly stuck; comparing Lee-Mykland to BNS statistics seems like dead end
Will attempt to find mistake in Lee-Mykland statistics
Attempt to develop system for analyzing jumps in overnight returns