The correlation between historical and realized volatilities is studied empirically for a large range of time intervals. Similarly, the correlation between the volatility changes and the realized volatilities is studied. Both quantities measure the response functions of the market participants....

This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the...

Estimates of daily volatility are investigated. Realized volatility can be computed from returns observed over time intervals of different sizes. For simple statistical reasons, volatility estimators based on high-frequency returns have been proposed, but such estimators are found to be strongly...

This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value...

This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory...

Time reversal invariance can be summarized as follows: no difference can be measured if a sequence of events is run forward or backward in time. Because price time series are dominated by a randomness that hides possible structures and orders, the existence of time reversal invariance requires...