Conditional Probability as a Measure of Volatility Clustering in Financial Time Series

Empirical analysis of time series of asset returns has revealed fat tails and volatility clustering which manifests itself as autocorrelations in absolute returns. We provide a quantitative measure of the well-studied phenomenon of volatility clustering in financial time series: We use the conditional probability distribution of the asset return, given the return in the previous time interval. Our analysis of a variety of data reveals a scaling collapse on to universal curve with a power-law tail at large returns. The scale factor provides a direct measure of volatility clustering. We introduce a phenomenological model which captures some of the key features of this scaling