We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al , and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.
This paper introduces an agent-based artificial financial market in which heterogeneous agents trade one single asset through a realistic trading mechanism for price formation. Agents are initially endowed with a finite amount of cash and a given finite portfolio of assets. There is no money-creation process; the total available cash is conserved in time.… (More)
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 are critically revised in the framework of theoretical… (More)
In high-frequency financial data not only returns, but also waiting times between consecutive trades are random variables. Therefore, it is possible to apply continuous-time random walks (CTRWs) as phenomenological models of the high-frequency price dynamics. An empirical analysis performed on the 30 DJIA stocks shows that the waiting-time survival… (More)
Continuous-time random walks can be used as phenomenological models of high-frequency time dynamics in financial markets. Empirical analyses show that the intertrade durations (or waiting-times) are non-exponentially distributed. This fact imposes constraints on agent-based models of financial markets based on continuous-double auctions.
The fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the Gnedenko-Kolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.
The recent financial crises pointed out the central role of public and private debt in modern economies. However, even if debt is a recurring topic in discussions about the current economic situation, economic modelling does not take into account debt as one of the crucial determinants of economic dynamics. Our contribution, in this paper, is to investigate… (More)
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 ÿnance. To this end, we compute the index volatility by means of the log-return standard deviation. We choose an hourly time window in… (More)