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 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. (Physica A 284 (2000) 376), and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future...

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...

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 the...

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 [4], and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE,...

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...

In this paper, we consider a new mathematical extension of the Black–Scholes (BS) model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed,...

This paper investigates the statistical behaviour of high-frequency index data from the Athens Stock Exchange. We find that 1min observations on the General Index of the Main Market for the three month period from 1 June 1998 to 10 September 1998 are characterised by very short run persistence...

This paper investigates the statistical behaviour of daily gold price data from 1971 to 2002. We find that the observations are characterised by short run persistence and scaling with a break point of 15 days, i.e., three working weeks. Daily returns are highly leptokurtic, with multi-period...