Inclusão do Decaimento Temporal na Metodologia Delta-Gama para o Cálculo do VaR de Carteiras Compradas em Opções no Brasil

The Value at Risk calculation for options has a lot of difficulties. The non-normality and the non-linearity of these assets cause sufficient unaccuracy in this measurement, mainly for the parametric models. The purpose of this article is to analyze the results of the VaR estimate for a portfolio of long options with two models: the Delta-Gama approach and the Delta-Gama-Theta approach, which considers the deterministic effect of the time decay when estimating the VaR. These methodologies are compared according to the moneyness and the maturity of the options and they are tested by the Christoffersen test and the Lopez test. The results show that the Delta-Gama-Theta methodology produces better results in the proportion-of-failures test for the VaR of 95%. Both methodologies produce large errors for the out-of-the-money options and for the options with short maturity.