1. Comparing Realized and Bi- Power Variation in Lee-Mykland Statistic Warren Davis April 11 Presentation

2. Outline Discussion of Lee-Mykland Change of Statistic Simulation Set-Up Simulation Results Future Directions

3. Lee and Mykland (2006)

4. The Bi-Power multiplied term in the denominator of the statistic was replaced by a simple realized variance, with a sum of returns squared, as was used in the BNS statistics earlier in the course This statistic was run on Bristol-Myers stock data, yielding 713 hits, as opposed to 1912 with the Bi-Power statistic.

5. Simulation Set-Up The following random variables were used: A set of normally distributed returns with mean=0, St. Dev.=.015 (95% of returns less than 3%) A random Poisson variable with mean.01 A normally distributed variable with mean 0, St. Dev.=.1 or.05

6. Simulation Set-Up The Poisson integers were multiplied by the second random normal distribution to create a series of jumps These jumps were added to the original normally distributed returns The Bi-Power and Realized Variance versions of Lee-Mykland were then ran on the data, seeing how accurately they performed in flagging jumps

7. Simulation Results- No Jumps Added Bi-Power ResultsRealized Variance Results # of Hits 28.03 7.54 (4.57)(2.68) % Returns Flagged.2803.0754 Bi-Power ResultsRealized Variance Results # of Hits 28.03 7.54 (4.57)(2.68)

8. Results- Poisson Integer Jumps % Correct Hits.98.17 99.05 Bi-Power ResultsRealized Variance Results % Hits False 10.60 3.07 % Jumps Missed.9569 1.609

9. Poisson x N(0,.0025) % Correct Hits 35.05 23.81 Bi-Power ResultsRealized Variance Results % Hits False 21.62 5.65 % Jumps Missed 62.67 76.19

10. Poisson x N(0,.01) % Correct Hits 53.33 32.76 Bi-Power ResultsRealized Variance Results % Hits False 19.31 4.47 % Jumps Missed 37.27 67.77

11. Future Directions GET RV TO WORK Explore iteration process of removing jumps, then retesting results Explore other estimators of local variance and test these, particularly exponential variations of bi-power