Estimación del valor en riesgo en la Bolsa Mexicana de Valores usando modelos de heteroscedasticidad condicional y teoría de valores extremos

This work proposes an approach for estimating value at risk (VaR) of the Mexican stock exchange index (IPC) by using a combination of the autoregressive moving average models (ARMA); three different models of the ARCH family, one symmetric (GARCH) and two asymmetric (GJR-GARCH and EGARCH); and the extreme value theory (EVT). The ARMA models were initially used to obtain uncorrelated residuals, which were later used for the analysis of extreme values. The GARCH, EGARCH and GJR-GARCH models, by including past volatility, are particularly useful both in instability and calm periods. Moreover, the asymmetric models GJR-GARCH and EGARCH handle differently the impact of positive and negative shocks in the market. The importance of the IPC in the Mexican economy raises the need to study its variations, particularly its downward movement; so, we propose to use VaR to calculate the maximum loss that IPC may have, at a certain level of reliability, in a given period of time, using more effici...