Evaluations of European options and stop-loss premiums via the Laplace transform inversion

Abstract In this work, a unified approach for evaluating the European Put and Call options as well as the Barrier options from exponential moments, the moment recovered-Laplace transform (MR-LT) inversion method is introduced. (see also [24] and [25]). In addition, the insurance stop-loss premium and the bivariate probability density function and corresponding tail distribution of aggregate claims are approximated. Several examples are considered to illustrate the accuracy of newly defined approximations.