Clustering of volatility as a multiscale phenomenon

The dynamics of prices in financial markets has been studied intensively bo th experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. Wha t is: well known is that absolute returns have memory on a long time range, this phenomenon is known as clustering of volatility. In this paper we sho w that volatility correlations are pou er-laws with a non-unique scaling ex ponent. This kind of multiscale phenomenology has some analogies with fully developed turbulence and disordered systems and it is now pointed out for financial series. Starting from historical returns series, we have also der ived the volatility distribution, and the results are in agreement with a l og-normal shape. In our study, we consider the New York Stock Exchange (NYS E), daily composite index closes (January 1996 to June 1998) and the US Dol lar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reser ve Bank of New York (October 1989 to September 1998).