Economics 201FS: Volatility and Jumps Grace Shuting Wei Spring 2011 20 April 2011 1
Feb 22, 2016
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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