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Examples of Multiscale Aspects of Volatility in Financial Markets

In this thesis we describe and evaluate a method for analysis of financial volatility. The method is originally presented in a paper by Michele Pasquini and Maurizio Serva from 1999. In that paper, the method is used to characterize American financial data from the NYSE composite index. Here we analyze Swedish financial data from Affarsvarldens All-Share index, and compare the result with that from the American data. The property of financial volatility that the method concerns is the autocorrelation structure for different moments of the volatility series. Pasquinis and Servas observation is that the volatility autocorrelation has a power-law structure, and that the exponent of the power-law is a non-linear function of the moment (of the volatility series) concerned. This study shows that the Swedish data is similar in nature to the American, but with generally stronger autocorrelation. This is shown to be the result, in part, by the extreme impact of the “Black Monday” 1987 on the American data. We also include a more detailed version of a proof presented in a paper by Michele Pasquini and Maurizio Serva from 2000, that theoretically motivates the above-mentioned method.