An Application of Extreme Value Theory for Measuring Financial Risk in BRICS Economies

Characterization and quantification of the tail behaviour of rare events is an important issue in financial risk management. In this paper, the extreme behaviour of stock market returns from BRICS over the period 1995–2015 is described using five parametric distributions based on extreme value theory, including two mixture distributions based on the student’s t distribution. The distributions are fitted to the data using the method of maximum likelihood. The generalized extreme value (GEV) distribution is found to give the best fit. Based on the GEV distribution, estimates of value at risk, $${\hbox {VaR}}_{p}(X)$$ VaR p ( X ) and expected shortfall, $${\hbox {ES}}_{p}(X)$$ ES p ( X ) from the five countries are computed. In addition, the correlation structure and tail dependence of these markets are characterized using several copula models. The Gumbel copula gives the best fit with evidence of significant relationships for all the pairs of the markets. To account for the possibility that due to sampling variability, a different model might be selected as the preferred model in a new sample from the same population, a short bootstrapping exercise was performed.