Testing option pricing with the Edgeworth expansion

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments. (C) 2004 Elsevier B.V. All rights reserved.

An extension of the linear delta expansion to superspace

We introduce and discuss the method of linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules. Calculations are carried out up to two loops and an expression for the optimized Kahler potential in the Wess-Zumino model is worked out.

Applicability of the linear delta expansion for the lambda phi(4) field theory at finite temperature in the symmetric and broken phases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Linear delta expansion applied to the O'Raifeartaigh model

We reassess the method of the linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules in the framework of the O'Raifeartaigh model for spontaneous supersymmetry breaking. The effective potential is calculated using both the fastest apparent convergence and the principle of minimal sensitivity criteria and the consistency and efficacy of the method are checked in deriving the Coleman-Weinberg potential.

Superspace approach to the renormalization of the O'Raifeartaigh model up to the second order in the linear delta expansion parameter

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Supergraph approach in a higher-order linear delta expansion calculation of the effective potential for F-type broken supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A metaheuristic to solve the transmission expansion planning

In this letter, a genetic algorithm (GA) is applied to solve - the static and multistage transmission expansion planning (TEP) problem. The characteristics of the proposed GA to solve the TEP problem are presented. Results using some known systems show that the proposed GA solves a smaller number of linear programming problems in order to find the optimal solutions and obtains a better solution for the multistage TEP problem.

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Quasicausal expansion of the quantum Liouville propagator

The quasicausal expansion of the quantum Liouville propagator is introduced into the Weyl-Wigner picture. The zeroth-order term is shown to lead to the statistical quasiclassical method of Lee and Scully [J. Chem. Phys. 73, 2238 (1980)].

Constructive heuristic algorithm for the DC model in network transmission expansion planning

A novel constructive heuristic algorithm to the network expansion planning problem is presented the basic idea comes from Garver's work applied to the transportation model, nevertheless the proposed algorithm is for the DC model. Tests results with most known systems in the literature are carried out to show the efficiency of the method.

Serotonergic mechanisms of the lateral parabrachial nucleus in renal and hormonal responses to isotonic blood volume expansion

This study investigated the involvement of serotonergic mechanisms of the lateral parabrachial nucleus (LPBN) in the control of sodium (Na+) excretion, potassium (K+) excretion, and urinary volume in unanesthetized rats subjected to acute isotonic blood volume expansion (0.15 M NaCl, 2 ml/100 g of body wt over 1 min) or control rats. Plasma oxytocin (OT), vasopressin (VP), and atrial natriuretic peptide (ANP) levels were also determined in the same protocol. Male Wistar rats with stainless steel cannulas implanted bilaterally into the LPBN were used. In rats treated with vehicle in the LPBN, blood volume expansion increased urinary volume, Na+ and K+ excretion, and also plasma ANP and OT. Bilateral injections of serotonergic receptor antagonist methysergide (1 or 4 mu g/200 eta 1) into the LPBN reduced the effects of blood volume expansion on increased Na+ and K+ excretion and urinary volume, while LPBN injections of serotonergic 5-HT2a/HT2c receptor agonist, 2.5-dimetoxi-4-iodoamphetamine hydrobromide (DOI;1 or 5 mu g/200 eta 1) enhanced the effects of blood volume expansion on Na+ and K+ excretion and urinary volume. Methysergide (4 mu g) into the LPBN decreased the effects of blood volume expansion on plasma ANP and OT, while DOI (5 mu g) increased them. The present results suggest the involvement of LPBN serotonergic mechanisms in the regulation of urinary sodium, potassium and water excretion, and hormonal responses to acute isotonic blood volume expansion.

Relief grating induced by photo-expansion in Ga-Ge-S and Ga-Ge-As-S glasses

We report the fabrication of relief diffraction gratings recorded on a surface of photosensitive Ga10Ge25S65 and Ga5Ge25As5S65 glasses by means of interference of two UV laser beams at 351 nm. The diffraction efficiency (eta) of first diffraction order was measured. Atomic-force-microscope (AFM) was used to perform a 3D imaging analysis of the sample surface topography that shows the superposition of an imprinted grating over the topography of the glass. The change in the absorption edge and the refractive index has been evaluated and a structural approach of the relief grating on the glass surface has been discussed.

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.

Transmission network expansion planning with security constraints

A mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints are presented. The methodology allows one to find an optimal and reliable transmission network expansion plan using a DC model to represent the electrical network. The security (n-1) criterion is used. The model presented is solved using a genetic algorithm designed to solve the reliable expansion planning in an efficient way. The results obtained for several known systems from literature show the excellent performance of the proposed methodology. A comparative analysis of the results obtained with the proposed methodology is also presented.