A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

Exogenous expectations on endogenous uncertainty: recursive equilibrium and survival

This paper analyses general equilibrium models with finite heterogeneous agents having exogenous expectations on endogenous uncertainty. It is shown that there exists a recursive equilibrium with the state space consisting of the past aggregate portfolio distribution and the current state of the nature and that it implements the sequential equilibrium. We establish conditions under which the recursive equilibrium is continuous. Moreover, we use the continuous recursive relation of the aggregate variables to prove that if the economy has two types of agents, the one who commits persistent mistakes on the expectation rules of the future endogenous variables is driven out of the market by the others with correct anticipations of the variables, that is, the rational expectations agents.

Essays in recursive equilibrium and market selection hypothesis

Este trabalho consiste em estudar modelos incluindo agentes com informação completa e incompleta sobre o ambiente econômico. Prova-se a existência de equilíbrio em que esses dois agentes coexistem e sob, algumas condições, obtêm-se que esse equilíbrio é recursivo e contínuo, ou seja, pode ser implementado por uma função contínua de transição que relaciona as variáveis de equilíbrio entre dois períodos consecutivos. Mostra-se, sob algumas hipóteses, que em equilíbrios recursivos contínuos, os agentes que cometem erros persistentes nas antecipações dos preços de equilíbrio são eliminados do mercado. Finalmente, exibimos diversos exemplos numéricos, no caso de mercados incompletos e informação completa, em que os agentes com expectativas racionais são eliminados do mercado. Usam-se métodos numéricos alternativos que possibilitam computar um equilíbrio em modelos com agentes heterogêneos.

Um teste de paridade coberta de juros, ajustada por prêmio de risco, para a economia brasileira entre 2007 e 2010

O conceito de paridade coberta de juros sugere que, na ausência de barreiras para arbitragem entre mercados, o diferencial de juros entre dois ativos, idênticos em todos os pontos relevantes, com exceção da moeda de denominação, na ausência de risco de variação cambial deve ser igual a zero. Porém, uma vez que existam riscos não diversificáveis, representados pelo risco país, inerentes a economias emergentes, os investidores exigirão uma taxa de juros maior que a simples diferença entre as taxas de juros doméstica e externa. Este estudo tem por objetivo avaliar se o ajustamento das condições de paridade coberta de juros por prêmios de risco é suficiente para a validação da relação de não-arbitragem para o mercado brasileiro, durante o período de 2007 a 2010. O risco país contamina todos os ativos financeiros emitidos em uma determinada economia e pode ser descrito como a somatória do risco de default (ou risco soberano) e do risco de conversibilidade percebidos pelo mercado. Para a estimação da equação de não arbitragem foram utilizadas regressões por Mínimos Quadrados Ordinários, parâmetros variantes no tempo (TVP) e Mínimos Quadrados Recursivos, e os resultados obtidos não são conclusivos sobre a validação da relação de paridade coberta de juros, mesmo ajustando para prêmio de risco. Erros de medidas de dados, custo de transação e intervenções e políticas restritivas no mercado de câmbio podem ter contribuído para este resultado.

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Pair trading in Bovespa with a quantitative approach: cointegration, Ornstein-Uhlenbeck equation and Kelly criterion.

Pair trading is an old and well-known technique among traders. In this paper, we discuss an important element not commonly debated in Brazil: the cointegration between pairs, which would guarantee the spread stability. We run the Dickey-Fuller test to check cointegration, and then compare the results with non-cointegrated pairs. We found that the Sharpe ratio of cointegrated pairs is greater than the non-cointegrated. We also use the Ornstein-Uhlenbeck equation in order to calculate the half-life of the pairs. Again, this improves their performance. Last, we use the leverage suggested by Kelly Formula, once again improving the results.

Rational expectations and the service of public debt: a recursive approach

This paper uses dynamic programming to study the time consistency of optimal macroeconomic policy in economies with recurring public deficits. To this end, a general equilibrium recursive model introduced in Chang (1998) is extended to include govemment bonds and production. The original mode! presents a Sidrauski economy with money and transfers only, implying that the need for govemment fmancing through the inflation tax is minimal. The extended model introduces govemment expenditures and a deficit-financing scheme, analyzing the SargentWallace (1981) problem: recurring deficits may lead the govemment to default on part of its public debt through inflation. The methodology allows for the computation of the set of alI sustainable stabilization plans even when the govemment cannot pre-commit to an optimal inflation path. This is done through value function iterations, which can be done on a computeI. The parameters of the extended model are calibrated with Brazilian data, using as case study three Brazilian stabilization attempts: the Cruzado (1986), Collor (1990) and the Real (1994) plans. The calibration of the parameters of the extended model is straightforward, but its numerical solution proves unfeasible due to a dimensionality problem in the algorithm arising from limitations of available computer technology. However, a numerical solution using the original algorithm and some calibrated parameters is obtained. Results indicate that in the absence of govemment bonds or production only the Real Plan is sustainable in the long run. The numerical solution of the extended algorithm is left for future research.

Dynamic hedging with stocastic differential utility

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires