Hedging options in a garch environment: testing the term structure of stochastic volatility models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P500 index volatility. U sing measurements of the ability of volatility models to hedge and value term structure dependent option positions, we fmd that hedging tests support the Black-Scholes delta and gamma hedges, but not the simple vega hedge when there is no model of the term structure of volatility. With various models, it is difficult to improve on a simple gamma hedge assuming constant volatility. Ofthe volatility models, the GARCH components estimate of term structure is preferred. Valuation tests indicate that all the models contain term structure information not incorporated in market prices.

Um estudo sobre os impactos da surpresa dos indicadores macroeconômicos de atividade e inflação no mercado futuro brasileiro de juros

As diretrizes de política monetária são definidas com base em resultados dos indicadores macroeconômicos divulgados ao mercado periodicamente. Os agentes deste mercado respondem rapidamente às alterações de cenário, com o objetivo de obter lucro ou evitar perdas financeiras expressivas. Com este motivacional, a proposta deste trabalho é avaliar como reage o mercado futuro de juros diante da divulgação de surpresas em determinados indicadores macroeconômicos, propondo um indicador de surpresa agregado para prever os impactos causados. Através dos dados extraídos da Bloomberg e da BM&F Bovespa, foi construída uma base de dados simplificada pela adoção de premissas para mensuração do impacto das surpresas divulgadas no preço do DI Futuro. A padronização dos parâmetros, a realização dos testes de média e as regressões otimizadas pelo método OLS possibilitaram ponderar os indicadores econômicos de acordo com a oscilação que os mesmos causam a este mercado. Por fim, o teste de comparação mostrou que o indicador de surpresa proposto foi mais eficiente nas previsões da reação do mercado do que um indicador que pondere de forma igualitária todos os indicadores macroeconômicos.

Simulation-based smoothing and filtering in factor stochastic volatility models : two econometric applications

In this article we use factor models to describe a certain class of covariance structure for financiaI time series models. More specifical1y, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. We build on previous work by allowing the factor loadings, in the factor mo deI structure, to have a time-varying structure and to capture changes in asset weights over time motivated by applications with multi pIe time series of daily exchange rates. We explore and discuss potential extensions to the models exposed here in the prediction area. This discussion leads to open issues on real time implementation and natural model comparisons.

Simulation -based smoothing and filtering in factor stochastic volatility models : two econometric applications (July-2001)

The past decade has wítenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events aI,"e country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions. In this article we measure the transmission of shocks by cross-market correlation\ coefficients following Forbes and Rigobon's (2000) notion of shift-contagion,. Our main contribution relies upon the use of traditional factor model techniques combined with stochastic volatility mo deIs to study the dependence among Latin American stock price indexes and the North American indexo More specifically, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. From a theoretical perspective, we improve currently available methodology by allowing the factor loadings, in the factor model structure, to have a time-varying structure and to capture changes in the series' weights over time. By doing this, we believe that changes and interventions experienced by those five countries are well accommodated by our models which learns and adapts reasonably fast to those economic and idiosyncratic shocks. We empirically show that the time varying covariance structure can be modeled by one or two common factors and that some sort of contagion is present in most of the series' covariances during periods of economical instability, or crisis. Open issues on real time implementation and natural model comparisons are thoroughly discussed.

Stabilization, volatility and the equilibrium real exchange rate

In a general equilibrium model. we show that the value of the equilibrium real exchange rate is affected by its own volatility. Risk averse exporters. that make their exporting decision before observing the realization of the real exchange rate. choose to export less the more volatile is the real exchange rate. Therefore the trude balance and the variance of the real exchange rate are negatively related. An increase in the volatility of the real exchange rate for instance deteriorates the trade balance and to restore equilibrium a real exchange rate depreciation has to take place. In the empirical part of the paper we use the traditional (unconditional) standard deviation of RER changes as our measure of RER volatility.We describe the behavior of the RER volatility for Brazil,Argentina and Mexico.Monthly data for the three countries are used. and also daily data for Bruzil. Interesting patterns of volatility could be associated to the nature of the several stabilization plans adopted in those countries and to changes in the exchange rate regimes .

Caracterização dos retornos e das volatilidades de ativos financeiros do mercado Brasileiro : uma abordagem baseada na volatilidade realizada

The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatilies measures, we attain the normality of the standardized returns, giving promise of improvements in Value at Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that the distributions of volatilities are nearly lognormal. Second, we estimate a simple linear model to the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in an out-of-sample experiment.

Forecasting multivariate time series under present-value-model short- and long-run co-movement restrictions

Using a sequence of nested multivariate models that are VAR-based, we discuss different layers of restrictions imposed by present-value models (PVM hereafter) on the VAR in levels for series that are subject to present-value restrictions. Our focus is novel - we are interested in the short-run restrictions entailed by PVMs (Vahid and Engle, 1993, 1997) and their implications for forecasting. Using a well-known database, kept by Robert Shiller, we implement a forecasting competition that imposes different layers of PVM restrictions. Our exhaustive investigation of several different multivariate models reveals that better forecasts can be achieved when restrictions are applied to the unrestricted VAR. Moreover, imposing short-run restrictions produces forecast winners 70% of the time for the target variables of PVMs and 63.33% of the time when all variables in the system are considered.

Automatic model selection for forecasting brazilian stock returns

This study aims to contribute on the forecasting literature in stock return for emerging markets. We use Autometrics to select relevant predictors among macroeconomic, microeconomic and technical variables. We develop predictive models for the Brazilian market premium, measured as the excess return over Selic interest rate, Itaú SA, Itaú-Unibanco and Bradesco stock returns. We nd that for the market premium, an ADL with error correction is able to outperform the benchmarks in terms of economic performance. For individual stock returns, there is a trade o between statistical properties and out-of-sample performance of the model.

Microfounded forecasting

Our focus is on information in expectation surveys that can now be built on thousands (or millions) of respondents on an almost continuous-time basis (big data) and in continuous macroeconomic surveys with a limited number of respondents. We show that, under standard microeconomic and econometric techniques, survey forecasts are an affine function of the conditional expectation of the target variable. This is true whether or not the survey respondent knows the data-generating process (DGP) of the target variable or the econometrician knows the respondents individual loss function. If the econometrician has a mean-squared-error risk function, we show that asymptotically efficient forecasts of the target variable can be built using Hansens (Econometrica, 1982) generalized method of moments in a panel-data context, when N and T diverge or when T diverges with N xed. Sequential asymptotic results are obtained using Phillips and Moon s (Econometrica, 1999) framework. Possible extensions are also discussed.

Automatic model selection for forecasting Brazilian stock returns

This study aims to contribute on the forecasting literature in stock return for emerging markets. We use Autometrics to select relevant predictors among macroeconomic, microeconomic and technical variables. We develop predictive models for the Brazilian market premium, measured as the excess return over Selic interest rate, Itaú SA, Itaú-Unibanco and Bradesco stock returns. We find that for the market premium, an ADL with error correction is able to outperform the benchmarks in terms of economic performance. For individual stock returns, there is a trade o between statistical properties and out-of-sample performance of the model.

Elections and stock market volatility: evidence in OECD countries and developing countries

Este trabalho estuda se existe impacto na volatilidade dos mercados de ações em torno das eleições nacionais nos países da OCDE e nos países em Desenvolvimento. Ao mesmo tempo, pretende, através de variáveis explicativas, descobrir os fatores responsáveis por esse impacto. Foi descoberta evidência que o impacto das eleições na volatilidade dos mercados de ações é maior nos países em Desenvolvimento. Enquanto as eleições antecipadas, a mudança na orientação política e o tamanho da população foram os factores que explicaram o aumento da volatilidade nos países da OCDE, o nível democrático, número de partidos da coligação governamental e a idade dos mercados foram os factores explicativos para os países em Desenvolvimento.

Options listing and the volatility of the underlying asset: a study on the derivative market function

Os mercados de derivativos são vistos com muita desconfiança por inúmeras pessoas. O trabalho analisa o efeito da introdução de opções sobre ações no mercado brasileiro buscando identificar uma outra justificativa para a existência destes mercados: a alteração no nível de risco dos ativos objetos destas opções. A evidência empírica encontrada neste mercado está de acordo com os resultados obtidos em outros mercados - a introdução de opções é benéfica para o investidor posto que reduz a volatilidade do ativo objeto. Existe também uma tênue indicação de que a volatilidade se torna mais estocástica com a introdução das opções.

Volatility of returns, variations in prices and volume traded: evidence from the main stocks in Brazil

We study the relationship between the volatility and the price of stocks and the impact that variables such as past volatility, financial gearing, interest rates, stock return and turnover have on the present volatility of these securities. The results show the persistent behavior of volatility and the relationship between interest rate and volatility. The results also showed that a reduction in stock prices are associated with an increase in volatility. Finally we found a greater trading volume tends to increase the volatility.