Aplicação do Modelo de Black, Derman & Toy à Precificação de Opções Sobre Títulos de Renda Fixa

Abstract

This paper presents an application of the model of Black, Derman & Toy related to the pricing of options of fixed income assets. The model is a non-stationary one, where the mean reversion or volatility reversion or both are functions of time. The model makes it possible to calculate the price of non-arbitrage derivative contracts of the term structure of interest rates. The fundamental hypothesis is that the interest rate follows a lognormal random walk. It uses a binomial tree to simulate the stochastic process in study. This tree is created in a way to be consistent with the initial interest rate curve observed by the market. The results obtained were consistent, however as this kind of option does not exist in Brazil, we could not compare the results of our tests with the market prices of the contracts.