In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties...

We show that the fluctuations of the tick-by-tick logarithmic price in a futures market can be described in terms of the Fokker–Planck equation (FPE). We calculate the corresponding drift and diffusion coefficients and argue that these values can contain some information pertaining to the...

In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of...

A general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations. Non-Poisson...

A detrended fluctuation analysis (DFA) is applied to the statistics of Korean treasury bond (KTB) futures from which the logarithmic increments, volatilities, and traded volumes are estimated over a specific time lag. In this study, the logarithmic increment of futures prices has no long-memory...

The price time series of the Italian government bonds (BTP) futures is studied by means of scaling concepts originally developed for random walks in statistical physics. The series of overnight price differences is mapped onto a one-dimensional random walk: the bond walk. The analysis of the...

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return...

It has been shown by Reed that random-sampling a Wiener process x(t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P(x(T))∼x(T)-β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling...

We analyse the time series of overnight returns for the BUND and BTP futures exchanged at LIFFE (London). The overnight returns of both assets are mapped onto a one-dimensional symbolic-dynamics random walk: The “bond walk”. During the considered period (October 1991–January 1994) the...

In this paper, the survival function of waiting times between orders and the corresponding trades in a double-auction market is studied both by means of experiments and of empirical data. It turns out that, already at the level of order durations, the survival function cannot be represented by a...