Statistical estimation of the Oscillating Brownian Motion

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew Brownian Motion, we propose two natural consistent estimators, which are variants of the integrated volatility estimator and take the occupation times into account. We show the stable convergence of the renormalized errors' estimations toward some Gaussian mixture, possibly corrected by a term that depends on the local time. These limits stem from the lack of ergodicity as well as the behavior of the local time at zero of the process. We test both estimators on simulated processes, finding a complete agreement with the theoretical predictions.Comment: 31 pages, 1 figur

A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data

In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous-time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Parameters estimated on the daily prices of 348 stocks of NYSE and S\&P 500, on different time windows, show consistent empirical evidence for leverageeffects. Mean-reversion effects are also detected, most markedly in crisis periods

Multi-scaling of moments in stochastic volatility models

We introduce a class of stochastic volatility models $(X_t)_{t \geq 0}$ for which the absolute moments of the increments exhibit anomalous scaling: \E\left(|X_{t+h} - X_t|^q \right) scales as $h^{q/2}$ for $q < q^*$, but as $h^{A(q)}$ with $A(q) q^*$, for some threshold $q^*$. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driven by a Levy subordinator and the characteristic measure of the Levy process has power law tails, then multi-scaling occurs if and only if the mean reversion is superlinear

The consistency of government deficits with macroeconomic adjustment : an application to Kenya and Ghana

Sustainable medium-term debt strategies are essential to adjustment programs committed to high growth and should be integrated into a consistent macroeconomic framework that encompasses debt, growth and strategies. This paper develops an analytical model that takes 2 steps. Its purpose is to analyze the relationship between the fiscal deficit, the real interest rate, the real growth rate and the real exchange rate - and to indicate what conditions would be necessary to stabilize a country's debt-to-GDP ratio in the long run. The authors analyze three fundamental concepts of deficit: cash (or observed), primary and operational. Applying the model to the empirical data for Kenya and Ghana, the author's reach the following conclusions. First, the fiscal effort in Kenya should have been somewhat stronger between 1980 and 1987. For the period 1988-91, the projected fiscal balance is broadly consistent with stabilization, and the same goal can be achieved with a lower inflation or growth rate. Secondly, in Ghana the average fiscal performance between 1980 and 1987 was only slightly weaker than it should have been. Projections for 1988-91 suggest that the government has substantial room to maneuver in its stabilization.Economic Stabilization,Economic Theory&Research,Environmental Economics&Policies,Macroeconomic Management,Banks&Banking Reform

A multivariate model for financial indices and an algorithm for detection of jumps in the volatility

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of Dow Jones Industrial Average and Financial Times Stock Exchange 100 in the period 1984-2013. Based on empirical results, we propose a bivariate version of the model, for which we find an explicit expression for the decay over time of cross-asset correlations between absolute returns. We compare our theoretical predictions with empirical estimates on the same financial time series, finding an excellent agreement.Comment: 20 pages, 22 figure

Nonlinear relativistic equation of state and phase transitions in nuclear matter at finite temperature and baryon density

The main goal of this Thesis, is the study of the thermodynamic properties of strongly interacting and dense nuclear matter, away from the nuclear ground state. This analysis constitutes one of the most interesting aspect and one of the major tasks in the modern high-energy nuclear physics. The first part of this dissertation, addresses the phenomenological and theoretical study of the nuclear matter equation of state, under the extreme conditions reached in high energy heavy ion collision experiments and in astrophysical object, such as for example neutron stars. Of particular interest is the determination of the microscopic hadronic and quark-gluon plasma equation of state in the framework of a relativistic mean field theory and in regime of high density and temperature. This is realized by means of a theoretical-computational approach and comparing the results with the recent experimental data obtained from the relativistic heavy ion collisions experiments. We adopt and develop a method based on the so-called non-extensive statistical mechanics to derive momentum and energy distribution functions to simply evaluate the physical quantities, taking into account of the correlations among the strongly interacting particles of the medium. Deconfinement phase transition is investigated by applying the Gibbs condition on a system of two (B, C) or three (B, C, S) conserved charges, by requiring the global conservation of each charges in the total phase. A multi-component system, in fact, implies a global and not a local charge conservation. Therefore, the charge densities ρB, ρC and ρS are fixed only as long as the system remains in one of the two pure phases. In the mixed phase, the charge concentration in each of the regions of one phase or the other may be different. We also study the strangeness production at finite temperature and baryon density by means of an effective relativistic mean-field model, with the inclusion of the full baryon octet and the meson degrees of freedom. In this context, lightest pseudo-scalar (π, K, K, η, η′) and vector mesons (ρ, ω, K∗, K∗, ϕ) are introduced in the QHD-Lagrangian density through an effective chemical potential depending on the self-consistent interaction between baryons. Hence, the obtained results are compared with those of minimal coupling scheme. The different meson ratios, strangeness production and possible kaon condensation are deeply investigated. Finally, in the last part of this dissertation, we investigate the possible thermodynamical instabilities in a warm (T ≤ 50 MeV) and dense nuclear medium (ρ0 ≤ ρB≤ 3ρ0), where a phase transition from nucleonic matter to resonance-dominated Δ matter can take place. This analysis is performed by requiring the global conservation of baryon and electric charge numbers in the framework of a relativistic equation of state. Similarly to the liquid-gas phase transition, we show that the nucleon-Δ matter phase transition is characterized by both mechanical instability ( fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the charge concentration) in asymmetric nuclear matter. We then perform an investigation and a comparative study on the different nature of such instabilities and phase transitions. In this context, the liquid-gas phase transition is also investigated in the framework of non-extensive statistical effects and in the last part of this analysis we also investigate the possible onset of strangeness-diffusive instability (fluctuation on the strangeness density) in a hot (70 ≤ T ≤ 140 MeV) and dense nuclear medium (ρ0 ≤ ρB≤ 3ρ0). The goal of this thesis, is therefore a deeper knowledge of the proprieties of nuclear matter at high density and finite temperature, with the study and the implementation of the nuclear equation of state through effective models (non-extensive statistical mechanics and effective relativistic mean-field model), through which overcome some theoretical and experimental difficulties in the determination of the physical parameters of the system. Finally, the study of the thermodynamical proprieties of strongly interacting nuclear matter, away from the nuclear ground state, allow us to deal and respond to one of the major questions of modern high-energy nuclear physic