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Second Attempt at Jump-Detection and Analysis Mike Schwert ECON201FS 2/13/08

Second Attempt at Jump-Detection and Analysis Mike Schwert ECON201FS 2/13/08. My Approach This Week

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Second Attempt at Jump-Detection and Analysis Mike Schwert ECON201FS 2/13/08

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  1. Second Attempt at Jump-Detection and Analysis Mike Schwert ECON201FS 2/13/08

  2. My Approach This Week • Last time, found too many jump days. Likely explanations include microstructure noise from using minute-by-minute prices and accidental inclusion of overnight returns in intraday calculations. • This time, rewrote code to sample prices at 5 minute frequency and exclude overnight returns. Recalculated summary statistics and number of jump days. • Examined effect of sampling frequency on jump detection by calculating z-statistics and counting jump days for 5, 10, 15, and 20 minute sampling frequencies. • Examined effect of sampling frequency on volatility calculations by creating volatility signature plots for realized variance and bipower variation.

  3. GE Stock Prices (5 minute frequency) Note: Closed at 39.28 on 9/10/01, opened at 35.50 on 9/17/01, bottomed out at 28.70 on 9/21/01

  4. Statistics Calculated Realized Variance: Bipower Variation: Relative Jump:

  5. Statistics Calculated Tri-Power Quarticity: Quad-Power Quarticity: Z-Statistic:

  6. Summary Statistics

  7. ZQP-max Statistics – 5 minute sampling frequency Number of jumps at 1% level of significance: 234 out of 2670 days (8.76%) Number of jumps at 0.1% level of significance: 84 out of 2670 days (3.15%) Number of jumps at 0.01% level of significance: 29 out of 2670 days (1.09%) Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

  8. ZQP-max Statistics – 10 minute sampling frequency Number of jumps at 1% level of significance: 186 out of 2670 days (6.97%) Number of jumps at 0.1% level of significance: 60 out of 2670 days (2.25%) Number of jumps at 0.01% level of significance: 17 out of 2670 days (0.64%) Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

  9. ZQP-max Statistics – 15 minute sampling frequency Number of jumps at 1% level of significance: 148 out of 2670 days (5.54%) Number of jumps at 0.1% level of significance: 42 out of 2670 days (1.57%) Number of jumps at 0.01% level of significance: 13 out of 2670 days (0.49%) Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

  10. ZQP-max Statistics – 20 minute sampling frequency Number of jumps at 1% level of significance: 141 out of 2670 days (5.28%) Number of jumps at 0.1% level of significance: 40 out of 2670 days (1.50%) Number of jumps at 0.01% level of significance: 11 out of 2670 days (0.41%) Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

  11. Volatility Signature Plots • Used idea introduced by Andersen, Bollerslev, Diebold, and Labys (1999). • Calculated mean daily realized variance and bipower variation over the sample period under sampling frequencies of 1 minute, 2 minutes, …, 30 minutes. • Plotted mean realized variance and bipower variation on the y-axis with sampling frequency on the x-axis. • RV and BV are higher for high-frequency samples because returns are distorted by microstructure noise such as bid-ask bounce. • RV and BV decrease as interval between samples increases because microstructure noise is cancelled out. • Must be wary of using too low of a sampling frequency, as sampling variation will affect volatility calculations. • Balance between sampling variation and microstructure noise appears to be reached around 15 minute sampling frequency.

  12. Volatility Signature Plot – Realized Variance

  13. Volatility Signature Plot – Bipower Variation

  14. Possible Extensions • Perform same calculations on S&P 100 index and stocks highly correlated with GE, or those with similar beta, or from a similar industry, etc. • Check whether GE jumps on the same days as these other assets. • Determine how much jumps are systematic vs. idiosyncratic. • Use volatility signature plots from several stocks to determine ideal sampling frequency for jump detection, if possible. • Incorporate ARCH, GARCH, or stochastic volatility models somehow?

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