Análise de componentes principais de dados funcionais - uma aplicação às estruturas a termo de taxas de juros

In this paper, we discuss the recent evolution of the domestic interest rate curves. Our approach is original, due to the fact that the data we used were observations of the values of the interest rate functions corresponding to particular arguments, the maturities associated with related instruments. We employ econometric techniques developed by Silverman and Ramsey among others, known as Functional Data Analysis. The results obtained are similar to several others found in the Literature. Specifically, we confirm the existence of three additive components, that have the same interpretation of Litterman& Sheinkman(1991).

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

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.