A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

A simple model to describe the thixotropic behavior of paints.

We propose a simple rheological model to describe the thixotropic behavior of paints, since the classical hysteresis area, which is usually used, is not enough to evaluate thixotropy. The model is based on the assumption that viscosity is a direct measure of the structural level of the paint. The model depends on two equations: the Cross-Carreau equation to describe the equilibrium viscosity and a second order kinetic equation to express the time dependence of viscosity. Two characteristic thixotropic times are differentiated: one for the net structure breakdown, which is defined as a power law function of shear rate, and an other for the net structure buildup, which is not dependent on the shear rate. The knowledge of both kinetic processes can be used to improve the quality and applicability of paints. Five representative commercial protective marine paints are tested. They are based on chlorinated rubber, acrylic, alkyd, vinyl, and epoxy resins. The temperature dependence of the rheological behavior is also studied with the temperature ranging from 5 ºC to 35 ºC. It is found that the paints exhibit both shear thinning and thixotropic behavior. The model fits satisfactorily the thixotropy of the studied paints. It is also able to predict the thixotropy dependence on temperature. Both viscosity and the degree of thixotropy increase as the temperature decreases.

Modulating the electronic structure of amino acids: interaction of model lewis acids with anthranilic acid

On the basis of theoretical B3LYP calculations, Yáñez and co-workers (J. Chem. Theory Comput. 2012, 8, 2293) illustrated that beryllium ions are capable of significantly modulating (changing) the electronic structures of imidazole. In this computational organic chemistry study, the interaction of this β-amino acid and five model Lewis acids (BeF1+, Be2+, AlF2(1+), AlF2+, and Al3+) were investigated. Several aspects were addressed: natural bond orbitals, including second order perturbation analysis of intra-molecular charge delocalization and the natural population analysis atomic charges; molecular geometries; selected infrared stretching frequencies (C-N, C-O, and N-H), and selected ¹H-NMR chemical shifts. The data illustrate that this interaction can weaken the H-O bond and goes beyond strengthening the intra-molecular hydrogen bond (N...H-O) to cause a spontaneous transfer of the proton to the nitrogen atom in five cases generating zwitterion structures. Many new features are observed. Most importantly, the zwitterion structures include a stabilizing hydrogen bond (N-H...O) that varies in relative strength according to the Lewis acid. These findings explain the experimental observations of α-amino acids (for example: J. Am. Chem. Soc. 2001, 123, 3577) and are the first reported fundamental electronic structure characterization of β-amino acids in zwitterion form.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

New simulation schemes for the Heston model

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma.

Survival of Lactobacillus plantarum in model solutions and fruit juices

The aim of the work was to study the survival of Lactobacillus plantarum NCIMB 8826 in model solutions and develop a mathematical model describing its dependence on pH, citric acid and ascorbic acid. A Central Composite Design (CCD) was developed studying each of the three factors at five levels within the following ranges, i.e., pH (3.0-4.2), citric acid (6-40 g/L), and ascorbic acid (100-1000 mg/L). In total, 17 experimental runs were carried out. The initial cell concentration in the model solutions was approximately 1 × 10(8)CFU/mL; the solutions were stored at 4°C for 6 weeks. Analysis of variance (ANOVA) of the stepwise regression demonstrated that a second order polynomial model fits well the data. The results demonstrated that high pH and citric acid concentration enhanced cell survival; one the other hand, ascorbic acid did not have an effect. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate, cranberry and lemon juice. The model predicted well the cell survival in orange, blackcurrant and pineapple, however it failed to predict cell survival in grapefruit and pomegranate, indicating the influence of additional factors, besides pH and citric acid, on cell survival. Very good cell survival (less than 0.4 log decrease) was observed after 6 weeks of storage in orange, blackcurrant and pineapple juice, all of which had a pH of about 3.8. Cell survival in cranberry and pomegranate decreased very quickly, whereas in the case of lemon juice, the cell concentration decreased approximately 1.1 logs after 6 weeks of storage, albeit the fact that lemon juice had the lowest pH (pH~2.5) among all the juices tested. Taking into account the results from the compositional analysis of the juices and the model, it was deduced that in certain juices, other compounds seemed to protect the cells during storage; these were likely to be proteins and dietary fibre In contrast, in certain juices, such as pomegranate, cell survival was much lower than expected; this could be due to the presence of antimicrobial compounds, such as phenolic compounds.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Correction of atmospheric delay effects in radar interferometry using a nested mesoscale atmospheric model

The temporal variability of the atmosphere through which radio waves pass in the technique of differential radar interferometry can seriously limit the accuracy with which the method can measure surface motion. A forward, nested mesoscale model of the atmosphere can be used to simulate the variable water content along the radar path and the resultant phase delays. Using this approach we demonstrate how to correct an interferogram of Mount Etna in Sicily associated with an eruption in 2004-5. The regional mesoscale model (Unified Model) used to simulate the atmosphere at higher resolutions consists of four nested domains increasing in resolution (12, 4, 1, 0.3 km), sitting within the analysis version of a global numerical model that is used to initiate the simulation. Using the high resolution 3D model output we compute the surface pressure, temperature and the water vapour, liquid and solid water contents, enabling the dominant hydrostatic and wet delays to be calculated at specific times corresponding to the acquisition of the radar data. We can also simulate the second-order delay effects due to liquid water and ice.

A dynamic causal model of the coupling between pulse stimulation and neural activity

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers. The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1–40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different. Following Friston, Mechelli, Turner, and Price (2000), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Antiferromagnetic spherical spin-glass model

We study the thermodynamic properties and the phase diagrams of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. It is a two-sublattice version of the ferromagnetic spherical p-spin glass model. We consider both the replica-symmetric and the one-step replica-symmetry-breaking solutions, the latter being the most general solution for this model. We find paramagnetic, spin-glass, antiferromagnetic and mixed or glassy antiferromagnetic phases. The phase transitions are always of second order in the thermodynamic sense, but the spin-glass order parameter may undergo a discontinuous change.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Systematics of nuclear densities, deformations and excitation energies within the context of the generalized rotation-vibration model

We present a large-scale systematics of charge densities, excitation energies and deformation parameters For hundreds of heavy nuclei The systematics is based on a generalized rotation vibration model for the quadrupole and octupole modes and takes into account second-order contributions of the deformations as well as the effects of finite diffuseness values for the nuclear densities. We compare our results with the predictions of classical surface vibrations in the hydrodynamical approximation. (C) 2010 Elsevier B V All rights reserved.