The analysis which assumes that tick by tick data is linear may lead to wrong conclusions if the underlying process is multiplicative. We compare data analysis done with the return and stock differences and we study the limits within the two approaches are equivalent. Some illustrative examples...

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion...

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which...

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...

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which...

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts 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...

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...

We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add...

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among...

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a...