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High frequency variability and microstructure bias

Friday 20th June 2008 - 15:30 to 16:10
INI Seminar Room 1
Microstructure noise can substantially bias the estimation of volatility of an Ito process. Such noise is inherently multiscale, causing eventual inconsistency in estimation as the sampling rate becomes more frequent. Methods have been proposed to remove this bias using subsampling mechanisms. We instead take a frequency domain approach and advocate learning the degree of contamination from the data. The volatility can be seen as an aggregation of contributions from many different frequencies. Having learned the degree of contamination allows us to frequency-by-frequency correct these contributions and calculate a bias-corrected estimator. This procedure is fast, robust to different signal to microstructure scenarios, and is also extended to the problem of correlated microstructure noise. Theory can be developed as long as the Ito process has harmonizable increments, and suitable dynamic spectral range.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons