Dresden 2003 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 2: Finanzm
ärkte und Risikomanagement II

AKSOE 2.3: Talk

Monday, March 24, 2003, 15:00–15:30, BAR/205

Forecasting Dynamical Cross Correlations — •Christof Reese and Bernd Rosenow — Institut für Theoretische Physik, Universität zu Köln, D-50923 Köln

The risk of an investment into the stock market is determined by both the volatilities of individual stocks and the correlations between these stocks. The volatility dynamics of individual stocks is characterized by volatility clustering which can be described by GARCH models which relate the present volatility to both past volatility and past innovations in stock prices.

While GARCH models have been quite successful in the univariate setting, their application to multivariate volatility forecasting for a large number of stocks has been hampered by both the difficulty to estimate the large number of model parameters and the poor performance of these models. Motivated by recent results [1, 2] we use methods of Random Matrix Theory (RMT) to suggest two classes of multivariate GARCH models which are able to describe correctly both the structure of correlations and their dynamics. We present empirical results using high frequency data of 118 stocks traded in the German stock market.

[1] P. Gopikrishnan, B. Rosenow, V. Plerou, and H.E. Stanley, Phys, Rev. E 64, R035106 (2001)

[2] B. Rosenow, V. Plerou, P. Gopikrishnan, and H.E. Stanley, Europhys. Lett. 59, 2002