Clustering of volatility as a multiscale phenomenon

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What 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 show that volatility correlations are pou er-laws with a non-unique scaling exponent. 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 derived the volatility distribution, and the results are in agreement with a log-normal shape. In our study, we consider the New York Stock Exchange (NYSE), daily composite index closes (January 1996 to June 1998) and the US Dollar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New York (October 1989 to September 1998).