Integración fraccionaria y valor en riesgo

Abstract

Recent studies on the volatility of stock markets stress problems associated with time varying correlations of prices and their implications to the stochastic behavior of returns. Numerous empirical approaches and models have been applied to examine that behavior, but emphasizing the case of the developed countries. Few studies have been devoted to identify the presence of long memory in emerging markets. This work is aimed to overcome such limitation through the examination of the long memory behavior of daily returns of the Mexican Stock Market Index for the period January 1983 to December 2009. ARCH family models are used to analyze the volatility of the market and an arfima (autoregressive fractionally integrated moving average) model is specified to model the returns. Estimations are made assuming different distributions for the errors (normal, Student t, and asymmetric Student t distributions). Then, the estimated volatilities are used to compute the Value at Risk (VaR) for both long and short positions. The empirical evidence confirms the presence of long memory manifested in the significant level of the fractional differencing parameter for the observed returns. This finding suggests the possibility of predicting future prices and obtaining abnormal profits, contrary to the assertions from the efficient markets theory. The analysis also suggests that the asymmetric volatility models could be better fitted to measure market risk, especially when a Student t skewed distribution is assumed for the error process