Avaliação de opções de troca e opções de spread européias e americanas

Abstract

This present paper aims at evaluating european and american exchange options and spread options. When the European options are considered, the model developed is based on Monte Carlo Simulations, taking into consideration the joint simulation of the underwriter’s price. The results of this model are compared with the premiums estimated by Margrabe (1978) and Kirk (1995) formulas. Additionally, the sensibility of the premiums relative to changes in some inputs parameters was analyzed, contributing for the correct understanding of these derivatives. When the american options are considered, the model developed consists in an adaption of the Least Square Monte Carlo (LSMC) method developed by Longstaff e Schwartz (2001), so as to contemplate the multidimensional case. The results presented by this model were then compared with that presented by two other models, based on pyramidal lattices, developed by Rubinstein (1994) and Brandimarte (2006). Besides comparing the results presented by these three models, the sensibility of the premiums relative to changes in some inputs parameters was analyzed, confirming the consistence of the results presented. It’s important to note that, different from the pyramidal lattices, the adaption of the LSMC model has the advantage to allow the extension for three or more underwriters.