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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 14: Financial Markets and Risk Management III

AKSOE 14.5: Vortrag

Donnerstag, 29. März 2007, 16:15–16:45, H8

Scaling behavior of Student-Lévy processes — •Oliver Grothe¹ and Rafael Schmidt² — ¹Research Training Group Risk Management, University of Cologne, Germany — ²Department of Economic and Social Statistics, University of Cologne, Germany

Student's t-distributions are widely used in financial studies as fat-tailed alternatives to normal distributions. However, as Student's t-distributions are not invariant under convolution, there are no Lévy processes with Student's t-marginals at all time points. As Oliveira et al. (2000) show, the convolution of two Student's t-distributions can well be approximated by Student's t-distributions with other parameters. Extending their approximation to a generalized Student-Levy process, however, violates the typical variance scaling property of the process. Following Heyde and Leonenko (2005), we focus on Lévy processes with Student's t-marginals at certain time points. We show, that a Student's t-approximation for the marginals is also suitable for other time horizons, while not exact. Using this approximation, we are able to describe the scaling behavior of the resulting generalized Student-Lévy processes. We provide an application of our approximation in the context of modelling high-frequency price returns.