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Seminar on Probability and Statistics Monday March 15 2010 Tokyo 002 3:00-4:00 pm
BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATIONS
Cecilia Mancini University of Florence Abstract
We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.
Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance. Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold. The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes. This talk is based on Mancini and Gobbi (2009), and Mancini (2010). |
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