Welfare costs of inflation: the case for interest-bearing money and empirical estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next. we extend this approach to ao economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Fmally, empirical estimates for Brazil are presented.

Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

Avaliação de métodos numéricos para precificação de derivativos: aplicação ao mercado brasileiro

Os objetivos deste trabalho foram (i) rever métodos numéricos para precificação de derivativos; e (ii) comparar os métodos assumindo que os preços de mercado refletem àqueles obtidos pela fórmula de Black Scholes para precificação de opções do tipo européia. Aplicamos estes métodos para precificar opções de compra da ações Telebrás. Os critérios de acurácia e de custo computacional foram utilizados para comparar os seguintes modelos binomial, Monte Carlo, e diferenças finitas. Os resultados indicam que o modelo binomial possui boa acurácia e custo baixo, seguido pelo Monte Carlo e diferenças finitas. Entretanto, o método Monte Carlo poderia ser usado quando o derivativo depende de mais de dois ativos-objetos. É recomendável usar o método de diferenças finitas quando se obtém uma equação diferencial parcial cuja solução é o valor do derivativo.

Avaliação de projetos na presença de volatilidade: estudo de caso de empresas no setor de telecomunicações

Quando as empresas decidem se devem ou não investir em determinado projeto de investimentos a longo prazo (horizonte de 5 a 10 anos), algumas metodologias alternativas ao Fluxo de Caixa Descontado (FCD) podem se tornar úteis tanto para confirmar a viabilidade do negócio como para indicar o melhor momento para iniciar o Empreendimento. As análises que levam em conta a incerteza dos fluxos de caixa futuros e flexibilidade na data de início do projeto podem ser construídos com a abordagem estocástica, usando metodologias como a solução de equações diferenciais que descrevem o movimento browniano. Sob determinadas condições, as oportunidades de investimentos em projetos podem ser tratados como se fossem opções reais de compra, sem data de vencimento, como no modelo proposto por McDonald-Siegel (1986), para a tomada de decisões e momento ótimo para o investimento. Este trabalho analisa a viabilidade de investimentos no mercado de telecomunicações usando modelos não determinísticos, onde a variável mais relevante é a dispersão dos retornos, ou seja, que a variância representa o risco associado a determinado empreendimento.

Exploratory semiparametric analysis of two-dimensional diffusions in finance

We examine bivariate extensions of Aït-Sahalia’s approach to the estimation of univariate diffusions. Our message is that extending his idea to a bivariate setting is not straightforward. In higher dimensions, as opposed to the univariate case, the elements of the Itô and Fokker-Planck representations do not coincide; and, even imposing sensible assumptions on the marginal drifts and volatilities is not sufficient to obtain direct generalisations. We develop exploratory estimation and testing procedures, by parametrizing the drifts of both component processes and setting restrictions on the terms of either the Itô or the Fokker-Planck covariance matrices. This may lead to highly nonlinear ordinary differential equations, where the definition of boundary conditions is crucial. For the methods developed, the Fokker-Planck representation seems more tractable than the Itô’s. Questions for further research include the design of regularity conditions on the time series dependence in the data, the kernels actually used and the bandwidths, to obtain asymptotic properties for the estimators proposed. A particular case seems promising: “causal bivariate models” in which only one of the diffusions contributes to the volatility of the other. Hedging strategies which estimate separately the univariate diffusions at stake may thus be improved.

WeIfare costs of inflation the case for interest-bearing money and empiricaI Estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next, we extend this approach to an economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Finally, empirical estimates for Brazil are presented.

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.