Comparison of VaR Models to the Brazilian Stock Market Under the Hypothesis of Serial Independence in Higher Orders: Are Garch Models Really Indispensable?

Abstract

Our objective in this article was to verify which models for the Value at Risk (VaR), among those that do not consider conditional volatility (Extreme Values Theory and the traditional Historical Simulation), and those that do consider it (GARCH and IGARCH), are adequate for the main index of the Brazilian stock market, the IBOVESPA. For this purpose, backtesting of adherence and the independence of first and higher orders were implemented for the four models mentioned, over forecast horizons of 1 and 10 days. The contribution is based on a the more rigorous criteria than those used in the literature for validating VaR models, as we performed backtesting for violation independence of higher orders on forecast horizons of 10 days. The results show that only GARCH family models were adequate. Thus, it is recommended to entities of the National Financial System that keep relevant positions in the Brazilian stock market, the utilization of internal risk models based on conditional volatility, in order to minimize the occurrence of violation clusters.

Keywords

• value at risk
• clusters of violations
• ibovespa