PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Manfred Denker, Jason Morton.

Title:The Estimation of Spot Volatility for High Frequency Data
Seminar:Seminar on Probability and its Application
Speaker:Axel Munk, University of Goettingen
Abstract:
In this talk estimation of the pathwise (spot) volatility is discussed for the price process of financial instruments which are traded at a high frequency. It is known that on small time scales classical (nonparametric) large scale approaches fail. Microstructure noise is one way to explain this and to model the small time scale bahaviour. In the first part of this talk we discuss Fourier series estimators for the problem of estimating a deterministic spot volatility in a microstructure noise model. We show that these obtain optimal convergence rates over Sobolev ellipsoids. In the second part we extend this to stochastic spot volatility. Due to the unknown smoothness of the spot volatility it becomes necessary to introduce locally adaptive estimators. To this end a specific thresholding for wavelets based on preaveraged observations will be used. The resulting estimator can be shown to be adaptive over a large range of Besov bodies. Our methods will be used to analyze price processes on small temporal scales and we show that various scaling paradoxes can be resolved. This is joint work with Marc Hoffmann (Paris IV) and Johannes Schmidt-Hieber (Goettingen University).

Room Reservation Information

Room Number:MB106
Date:12 / 10 / 2010
Time:02:30pm - 03:25pm