Existence and uniqueness of a fixed-point for local contractions

This paper proves the existence and uniqueness of a fixed-point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.

The performance of open-end Brazilian fixed income mutual funds for retail clients

From a financial perspective, this dissertation analyzes the Brazilian mutual fund industry performance for an average retail client. The most representative funds for the local population, that are the fixed income open-end ones, will be selected and their performance will be measured aiming to answer if clients of this industry obtained a proper return over their investments in the period between August 2010 and August 2013. A proper return will be understood as the preservation of the purchasing power of the individual´s savings, what is achieved with a positive performance of a mutual fund after discounting taxes, administrative fees and inflation. After obtaining an answer for the previous question, this dissertation will explore a possible alternative solution: Tesouro Direto, that is an example of a financial approach that could foster the disintermediation between savings and investments through electronic channels. New electronic platforms, with a broader scope, could be utilized to increase the efficiency of funding productive investments through better remunerating Brazilian savings. Tesouro Direto may point towards a new paradigm.

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.