Bootstrap prediction in univariate and multivariate volatility models

Abstract

The goals of the thesis aims is to propose, based on existing procedures for the univariate case, procedures for bootstrap prediction intervals in multivariate volatility models (multivariate GARCH and multivariate stochastic volatility models, with and without leverage effect). The interest in multivariate models comes from the fact that, as it is known in financial literature, there is a dependency structure between the financial series, since the volatility of different assets from the same or different markets move together. The interest in the multivariate models with leverage effect, in turn, stems from the fact that, as is well known in financial markets, the negative returns have greater influence on volatility than positive returns of the same magnitude. The project considers several multivariate GARCH models, generalizations of the models leverage GARCH, EGARCH and GJR for the multivariate case and multivariate stochastic volatility model. The thesis will present the algorithms for each model as well as a study, through simulations, the behavior of the proposed procedure for assessing the quality of the prediction intervals obtained for the returns of the individual series and an investment portfolio. Applications will also be conducted with a series of Brazilian and non-Brazilian financial series.