Regensburg 2010 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 23: Financial Markets and Risk Management III

SOE 23.4: Vortrag

Freitag, 26. März 2010, 12:00–12:30, H44

Tracking volatility with higher-order-correlation nonlinear filters — •Oliver Grothe — Department of Economic and Social Statistics, University of Cologne, Germany

A challenging task in financial risk management is the real-time estimation and tracking of hidden parameters of stochastic processes such as price processes. The classical way to estimate latent states is to apply the linear Kalman filter. When interested in sequential estimates of parameters, however, the filtering problem turns out to be nonlinear and thus nonlinear filters have to be applied. Developed for problems in physics and engineering, the basic idea of these filters is to linearize the nonlinear problems, leading to approximations of densities and equations. The computationally most attractive filters for real-time applications are the Gaussian filters.

However, Gaussian filters are not able to sequentially estimate parameters that are not linearly correlated with the measurement. In financial applications, such parameters are stock price volatility or variance, which are of central interest for risk management.

In order to nevertheless estimate such parameters, we extend the standard Gaussian filters with a higher-order-correlation update and the propagation of asymmetric dependence structures. We call this filter type higher-order-correlation filter. We show the validity of our approach in applying it to ultra-high frequency stock price data and to estimate parameters of an Ornstein-Uhlenbeck model.