Clustering of volatility as a multiscale phenomenon

TL;DR

This paper investigates the multiscale nature of volatility clustering in financial markets, revealing power-law correlations and a log-normal distribution of volatility, with empirical analysis on NYSE and USD-DM data.

Contribution

It demonstrates that volatility correlations follow power-laws with non-unique exponents and derives a log-normal volatility distribution from historical data.

Findings

Volatility correlations exhibit power-law behavior.

Volatility distribution is consistent with a log-normal shape.

Multiscale phenomenology similar to turbulence is observed.

Abstract

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 it 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 power-laws with a non-unique scaling exponent. This kind of multiscale phenomenology, which is well known to physicists since it is relevant in fully developed turbulence and in disordered systems, is recently 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 1966 to June 1998) and the US Dollar/Deutsch Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New York (October 1989 to September 1998).