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...

High-frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well established by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is...

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...

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time....

In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later, we study the case of...

Recent single-molecule fluorescence spectroscopy have been analyzed in terms of a reaction with a single fluctuating rate (Shenter, J. Phys. Chem A 103 (1999) 10477). The fluctuations in that analysis are related to the solution of an O–U equation. We propose the use of a simpler type of...

We develop the formalism for a continuous-time generalization of the persistent random walk, by allowing the sojourn time to deviate from the exponential form found in standard discussions of this subject. This generalization leads to evolution equations, in the time domain, that differ and are...

We present a method for finding statistical properties of the first passage time to exit an interval of general diffusion processes subject to random delta function impulses. Exact solutions are found for the mean first passage time for Brownian motion. Other special cases, detailed in the text,...

All definitions and analyses of the one-dimensional telegrapher's equation assume an underlying translational invariant space. We here generalize this model to allow for non-uniform spatial properties, and derive the form of the backward equation and the associated boundary conditions in the...