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Economics 201FS: Volatility and Jumps

Grace Shuting WeiSpring 2011

20 April 2011

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Investigating volatility during jumps• Previously

– BNS test– Ait-Sahalia and Jacod (2008)

• This week– Regression of test statistics from Ait-Sahalia and Jacod– Direction of jumps

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Ait-Sahalia and Jacod (2008)• Multipower variation

• Test statistic

• Intuition: When power is large (p >2), the contribution of jumps to B(p) overwhelms everything else. This is because high powers (p >2) magnify the large increments at the expense of the small ones.

• Asymptotic values

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FDX: A-J Jump Test

Intercept Coefficient P-val 1 P-val 2RV 0.4888 -0.0146 0.0000 0.4582BV 0.4454 -0.0007 0.0000 0.9724

MedV 0.4825 -0.0128 0.0000 0.5070MinV 0.4784 -0.0115 0.0000 0.5500

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UPS: A-J Jump Test

Intercept Coefficient P-val 1 P-val 2RV 0.2442 0.0532 0.0000 0.0044BV 0.1895 0.0737 0.0004 0.0001

MedV 0.2164 0.0643 0.0001 0.0008MinV 0.2149 0.0648 0.0001 0.0007

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SPFU: A-J Jump Test

Intercept Coefficient P-val 1 P-val 2RV 0.1569 0.1546 0.0000 0.0000BV 0.1822 0.1470 0.0000 0.0000

MedV 0.1909 0.1443 0.0000 0.0000MinV 0.2007 0.1410 0.0000 0.0000

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Bollerslev, Todorov, and Zheng (2011)• Time-of-Day measures the ratio of the diffusive variation over different

parts of the day relative to its average value for the day.

• Threshold type test

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FDX: BTZ Jump Test

RV

Positive 25.3034

Negative 24.8800

Cont 24.9167

CV

Positive 21.0427

Negative 20.6837

Cont 22.0098

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UPS: BTZ Jump Test

RVPositive 26.3374

Negative 18.9684

Cont 25.2703

CV

Positive 15.7311

Negative 15.6091

Cont 16.5947

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SPFU: BTZ Jump Test

RVPositive 14.4031

Negative 14.2236

Cont 14.9952

CV

Positive 12.3647

Negative 12.2311

Cont 13.7115