A técnica da transformada integral generalizada aplicada na solução da equação de black-scholes para avaliação de derivativos

Abstract

The Generalized Integral Transform Technique (GITT), analytic-numerical method based on orthogonal eigenfunctions expansions, was used to solve the Black Scholes equation (BSE) that is frequently applied in financial areas, more specifically in valuation of call or put options. The Generalized Integral Transform Method was used in (BSE) accomplish the comparation between results obtained by algorithm implemented computationally in the programs: Mathematica and Fortran by DIVPAG in the library IMSL with other results presented in researches generated through of numerical techniques like the finite difference method. In this sense the viability of the technique application was be evaluated. The development of the algorithm was possible doing some changes in variables in the (BSE) and using one suitable eigenvalue problems to search solutions. The results obtained by GITT was compared to papers presents in the current literature, and displayed in terms of the asset value through of call or put options varying between american and european conditions that distinguish themselves in relation of the exercise moment in the option, to different values of volatility, presenting good agreement with availables papers, substanting the viability of the GITT use to get the solutions to BSE problem.