Closed Formula for Options with Discrete Dividends and Its Derivatives

Abstract

We present a closed pricing formula for European options under the Black–Scholes model as well as formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and a proposition that relates expectations of partial derivatives with partial derivatives themselves. The closed formulas are attained assuming the dividends are paid in any state of the world. The results are readily extensible to time-dependent volatility models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis, covering calls and puts, together with results on their partial derivatives. The closed formulas presented here allow a fast calculation of prices or implied volatilities when compared with other valuation procedures that rely on numerical methods.     

Homogeneous and non-homogeneous boundary value problems for first order linear hyperbolic systems arising in fluid mechanics (Part II)

We prove the existence and the uniqueness of differentiable and strong solutions for a class of boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids. In particular necessary and sufficient conditions for the existence of solutions for the non-homogeneous problem are studied; strong solutions are obtained without this supplementary condition. See Theorems3.2, 3.9, 4.1, 4.2 and Corollary 4.3; see also the discussion after Theorem 4.1. In particular we don't assume the boundary space to be maximal non-positive and the boundary matrix to be of constant rank on the boundary. In this paper we prove directly the existence of differentiable solutions without resort to weak or strong solutions. An essential tool will be the introduction of a space Z of regular functions verifying not only the assigned boundary conditions but also some suitable complementary boundary conditions; see also the introduction of Part I of this work [I].     

Homogeneous and non-homogeneous boundary value problems for first order linear hyperbolic systems arising in fluid-mechanics (Part I)

We prove t h e existence and the uniqueness of differentiable and strong solutions for aclass of non-homogeneous boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids . The method provides.the existence of differentiable solutions without resorting to strong or weak solutions. A necessary and sufficient condition for the existence of solutions for the non-homogeneous problem is proved. I t consists of an explicitrelationship between the boundary values of u and those of the data f . Strong solutions are obtained without this supplementary assumption. See Theorems 3.1, 4.1, 4 . 2 , 4.3 and Corollary 4.4; see also Remarks 2.1 and 2.4. In this paper we consider equation (3.1) below. In the forthcoming part II we prove similar results for the corresponding evolution problem.     

Higher order symmetrizer and application to an unusual transport equation

We study a class of stationary transport equation with nonlocal low-order tems We obtain the existence and uniqueness of a solution in sobolev spaces     

Analysis of degradation phenomena in ancient,traditional and improved building materials of historical monuments

A review is presented on constructive techniques plus materials and the processes involved in degradation phenomena observed in two historical monuments: the Zambujeiro dolmen (Portugal) and the Roman Aqueduct of Carthage (Tunisia). Dolmens are particularly impressive megalithic constructions for the dimensions of granite blocks. At Zambujeiro, the upright stones have undergone a catastrophic evolution after the archaeological exploitation due to accelerated weathering through a process apparently distinct from natural granite decay in nearby outcrops. The biological attack of granite minerals by lichen exudates has emphasized the hazardous character of bromine and more has been learnt about construction techniques, namely, the insertion in the mound of an impermeable clay stratum that hinders water penetration into the dolmen chamber. The characterization of original Roman ashlar blocks, including masonry and the diagnosis of Byzantine and medieval reconstruction testimonies in the Aqueduct of Carthage were the object of a detailed study by X-ray diffraction and synchrotron radiation X-ray fluorescence. Traditional constructive techniques and local construction materials were studied and successive historical, modern and recent rehabilitations were reappraised. PACS  83.80.Nb; 64.70.Kb; 78.70.En; 41.60.Ap     

Virtual element methods for parabolic problems on polygonal meshes

The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate complex nonpolynomial functions on the elements and preserving an optimal order of convergence. In this article, we develop for the first time, the VEM for parabolic problems on polygonal meshes, considering time‐dependent diffusion as our model problem. After presenting the scheme, we develop a theoretical analysis and show the practical behavior of the proposed method through a large array of numerical tests. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2110–2134, 2015     

A Zn(II) luminescent complex with a Schiff base ligand: solution,computational and solid state studies

Abstract

A new mononuclear complex of zinc(II), [Zn(HL)₂]?2DMF (H₂L = (E)-N′-((E)-(hydroxyimino)butan-2-ylidene)salicyloylhydrazide, DMF = N,N-dimethylformamide), was prepared and characterized. Single-crystal X-ray crystallography revealed a six-coordinate zinc(II) surrounded by nitrogen of the oxime function and oxygen and distal nitrogens of the acylhydrazone group. This entity also exists in solution as demonstrated by ¹H-NMR and potentiometric titrations. The computational analysis showed that the molecular orbitals involved in the main electronic transitions of the complex species in solution are centered on the ligand with negligible contribution of the metal ion. The photophysical properties of the complex were evaluated in solution and in the solid state. Luminescence studies showed that the solid has a strong emission at 550 nm with a large Stokes shift with respect to absorption. The solid state fluorescence emission is ascribed to ligand-centered and/or ligand-to-ligand charge transfer transitions, following the DFT results in solution. A comparison with a previously reported mononuclear [Zn(HL)₂] allowed the investigation of the influence of DMF molecules in the structural packing and the luminescence properties.     

A comparison of the magnetic structures of KMn(4)(PO(4))(3) and KCo(4)(PO(4))(3) based on the connectivity of the coordination polyhedra

The crystal structures of KMn(4)(PO(4))(3) and KCo(4)(PO(4))(3) have been determined by neutron diffraction at room temperature. Both compounds are orthorhombic with similar cell parameters, but they crystallize in different space groups, Pnam for the Mn phosphate and Pnnm for the Co analogue. On the basis of the metal cation polyhedra and their connectivity, the crystal structures have been rationalised, which allow interpretation of the main magnetic interactions between them. Magnetic measurements show ferromagnetic behaviour for the Co compound, whereas in the Mn derivative antiferromagnetism is observed. Both magnetic structures are described and qualitatively analysed in terms of superexchange and super-superexchange interactions.     

Quenching of local magnetic moment in oxygen adsorbed graphene nanoribbons

The electronic and magnetic properties of oxidized zigzag and armchair graphene nanoribbons, with hydrogen passivated edges, have been investigated from ab initio pseudopotential calculations within the density functional scheme. The oxygen molecule in its triplet state is adsorbed most stably at the edge of a zigzag nanoribbon. The Stoner metallic behavior of the ferromagnetic nanoribbons and the Slater insulating (ground state) behavior of the antiferromagnetic nanoribbons remain intact upon oxygen adsorption. The formation of a spin-paired C-O bond drastically reduces the local atomic magnetic moment of carbon at the edge of the ferromagnetic zigzag ribbon.     

High precision delta(17)O isotope measurements of oxygen from silicates and other oxides: method and applications

The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd.