Scaling in Stock Market Data: Stable Laws and Beyond

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Abstract
The concepts of scale invariance and scaling behavior are now increasingly applied outside their traditional domains of application, the physical sciences. Their application to financial markets, initiated by Mandelbrot in the 1960s, has experienced a regain of interest in the recent years, partly due to the abundance of high-frequency data sets and availability of computers for analyzing their statistical properties. This lecture is intended as an introduction and a brief review of current research in a field which is increasingly applied in the study of time aggregation properties of financial data. We will try to show how the concepts of scale invariance and scaling behavior may be usefully applied in the framework of a statistical approach to the study of financial data, pointing out at the same time the limits of such an approach.