We use three stochastic games for the wealth of economic agents which may be at work in a real economy and we derive their statistical equilibrium distributions. Based on a heuristic argument, we assume that the expected observed wealth distribution is a mixture of these three distributions. We...

In this paper, a simulation of high-frequency market data is performed with the Genoa Artificial Stock Market. In the market model, heterogeneous agents trade a risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget...

We study the volatility of the MIB30–stock–index high–frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous–time finance. To this end, we compute the index volatility by means of...

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...