In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifra
ctal model (MSM). In order to see how well the estimated models capture the temporal dependence of the data, we estimate and compare the scaling exponents $H(q)$ (for $q = 1, 2$) for both empirical data and simulated data of the estimated MSM models. In most cases the multifractal model appears to generate `apparent long memory in agreement with the empirical scaling laws.
A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpre
ted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firms technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Fore
ign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.
At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour i
s illustrated using LIBOR data, and a possible martingale pricing scheme is discussed.
An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the collective be
havior of the stochastic fluctuations of these time-series which is investigated by using a clustering linkage procedure. Without any a priori assumption, we individuate a meaningful separation in 6 main clusters organized in a hierarchical structure.
We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of t
he underlying network and in particular we verify that scale free networks generate distributions with power-law tails in the high-income region. Numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self-consistent solution. We show that empirical data for the income distribution in Australia are qualitatively well described by our theoretical predictions.
The discovery of hard, power-law X-ray emission from a sample of six nearby elliptical galaxies, including the dominant galaxies of the Virgo,Fornax and Centaurus clusters (M87, NGC 1399 and NGC 4696, respectively), and NGC 4472, 4636 and 4649 in the
Virgo cluster, has important implications for the study of quiescent supermassive black holes. We describe how the broad band spectral energy distributions of these galaxies, which accrete from their hot gaseous halos at rates comparable to their Bondi rates, can be explained by low-radiative efficiency accretion flows in which a significant fraction of the mass, angular momentum and energy is removed from the flows by winds. The observed suppression of the synchrotron component in the radio band and the systematically hard X-ray spectra, which are interpreted as thermal bremsstrahlung emission, support the conjecture that significant mass outflow is a natural consequence of systems accreting at low-radiative efficiencies. We briefly discuss an alternative model for the X-ray emission, namely that it is due to nonthermal synchrotron-self Compton processes in the accretion flow, or wind. This appears to require implausibly weak magnetic fields. Emission from a collimated jet viewed off axis should be distinguishable from the bremsstrahlung model by variability and thermal line emission studies. We argue that the difference in radiative efficiency between the nuclei of spiral and elliptical galaxies arises from the different manner in which interstellar gas is fed into the nuclei. In ellipticals, matter fed from the hot (slowly cooling) ISM is likely to be highly magnetized and with low specific angular momentum, both of which favor low-radiative efficiency accretion solutions and possibly the formation of the observed jets.
We present a model for the different X-ray spectral states displayed by Galactic Black Hole Candidates (GBHC). We discuss the physical and spectral implications for a magnetically structured corona in which magnetic flares result from reconnection of
flux tubes rising from the accretion disk by the magnetic buoyancy instability. Using observations of one of the best studied examples, GX339-4, we identify the geometry and the physical conditions characterizing each of these states. We find that, in the Soft state, flaring occurs at small scale heights above the accretion disk. The soft thermal-like spectrum is the result of heating and consequent re-radiation of the hard X-rays produced by such flares. The hard tail is produced by Comptonization of the soft field radiation. Conversely, the hard state is the result of flares triggered high above the underlying accretion disk which produce X-rays via Comptonization of either internal synchrotron radiation or soft disk photons. The spectral characteristics of the different states are naturally accounted for by the choice of geometry: when flares are triggered high above the disk the system is photon-starved, hence the hard Comptonized spectrum of the hard state. Intense flaring close to the disk greatly enhances the soft-photon field with the result that the spectrum softens. We interpret the two states as being related to two different phases of magnetic energy dissipation. In the Soft state, Parker instability in the disk favours the emergence of large numbers of relatively low magnetic field flux tubes. In the hard state, only intense magnetic fields become buoyant. The model can also qualitatively account for the observed short timescale variability and the characteristics of the X-ray reflected component of the hard state.
It is believed that most giant elliptical galaxies possess nuclear black holes with masses in excess of $10^8Msun$. Bondi accretion from the interstellar medium might then be expected to produce quasar-like luminosities from the nuclei of even quiesc
ent elliptical galaxies. It is a puzzle that such luminosities are not observed. Motivated by this problem, Fabian & Rees have recently suggested that the final stages of accretion in these objects occurs in an advection-dominated mode with a correspondingly small radiative efficiency. Despite possessing a long-known active nucleus and dynamical evidence for a black hole, the low radiative and kinetic luminosities of the core of M87 provide the best illustration of this problem. We examine an advection-dominated model for the nucleus of M87 and show that accretion at the Bondi rate is compatible with the best known estimates for the core flux from radio through to X-ray wavelengths. The success of this model prompts us to propose that FR-I radio galaxies and quiescent elliptical galaxies accrete in an advection dominated mode whereas FR-II type radio-loud nuclei possess radiatively efficient thin accretion disks.
