The definition of time is still an open question when one deals with high frequency time series. If time is simply the calendar time, prices can be modeled as continuous random processes and values resulting from transactions or given quotes are discrete samples of this underlying dynamics. On...

The definition of time is still an open question when one deals with high frequency time series. If time is simply the calendar time, prices can be modeled as continuous random processes and values resulting from transactions or fixings are discrete samples of this underlying dynamics. On the...

We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $\sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=\sigma(t) \omega(t)$ where...

The dynamics of prices in stock markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, while the distribution of returns of the most important indices is known to be a truncated Lévy, the behaviour of volatility correlations is still...

Prediction of events is a challenge in many different disciplines, from meteorology to finance: the more difficult this task is, the more complex the system is. Nevertheless, even according to this restricted definition, a general consensus on what should be the correct indicator for complexity...

In this paper we compute exactly the ground state energy and entropy of the dilute ferromagnetic Ising model. The two thermodynamic quantities are also computed when a magnetic field with random locations is present. The result is reached in the replica approach frame by a class of replica order...

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. Under the...

In this work we discuss the problem of price definition when using high frequency foreign exchange data. If one uses the spot mid price a strong autocorrelation of returns, at one lag, is found which is only due to microstructure effect and does not capture the real behavior of price dynamics....

The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter as a function of the dilution coefficient. An analogous exact solution is obtained in the presence of a magnetic field with random locations. Results lead to a complete...