We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non-Markovian formulation of the CTRW aimed to...

An analysis based on the assumption that tick-by-tick data is linear may lead to incorrect conclusions if the underlying process is multiplicative. We compare data analysis done with return and stock differences and study the limits within which the two approaches are equivalent. Illustrative...

The present work briefly summarizes the results obtained in Palatella et al. Eur. Phys. J. B 38 (2004) 671 using the Diffusion Entropy technique and adds some new results regarding the Dow Jones Index time series. We show that time distances between peaks of volatility or activity are...

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount...

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which amounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return...

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted...

The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many...

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market...