Jump in Returns & Jump in Volatility

1. Jump in Returns & Jump in Volatility Kyu Won Choi March 22, 2011

2. Data Set • S&P 500 • 1997/1/2 – 2010/12/30 (3482 trading days) • 1-min frequency prices from 9:35am to 3:59pm • Extracted prices from 2003/9/22 to 2008/12/31 (1316 trading days) • For 5-min RV & BV & TV (jump detection) alone (76 returns per day) • VIX • 2003/9/22 – 2008/12/31 (5-min prices) • Though the same time period, inconsistent number of trading days (?)

3. Outline • Focus on Truncated Variance to detect the Jump in S&P 500 Index • Jump in VIX using Power Variation • Realized Correlation & T-statistics

4. S&P 500 Index

5. Realized Variance & Bipower Variance

6. Realized Variance & Truncated (Threshold) Variance

7. Truncated (Threshold) Variance3 SDs & 2SDs

8. Jump Contribution (BV and 4ST TV)

9. Jump Contribution(3SD and 2SD TV)

10. VIX Index

11. VIX: Power Variation (p = 2)

12. VIX : Power Variation (p=3,p=4)

13. VIX Power Variation (p=1, c=1,1.5)

14. Activity Index (Todorov, Tauchen 2010) • Activity Signature Function (ASF) behaves differently for the process • Continuous processes • Continuous + jump processes • Pure jump processes • Pure Jump Process from QASF, 5-min (Todorov, Tauchen 2010)

15. Jump in Returns and Volatility • Realized Correlation between jumps in two series • T-statistics

16. Realized Correlation

17. Problems • Incorrect results because of the data/coding problem? • Starting with 2003, the data clearing • VIX data • extra 11/28, 12/24, 12/26 (that SPFU does not have) • Some days, missing the 5-min price data • SPFU • fixed closing price: 5-minute frequency (to be consistent ) • Analyze the results year by year • During the times of market stress, is the correlation between jump in price and volatility higher than other times?

18. Realized Correlation (2003)

19. T-statistics