A Coupling of Extreme-Value Theory and Volatility Updating with Value-at-Risk Estimation in Emerging Markets: A South African Test

Abstract

This research is aimed at a formal appraisal of recent advancements in stochastic volatility modeling and extreme-value theory to application of value-at- risk computation in particularly volatile markets. Established methods such as historical simulation are prone to underestimating value-at-risk in such developing markets. Two contemporary methods of value-at-risk calculation are tested on a representative portfolio of South African stocks. The first method incorporates extreme value theory. The second model includes both extreme value theory and volatility updating (via GARCH-type modeling). The combined GARCH-type time-series approach and extreme value theory model is found to provide significantly better results than both straightforward historical simulation as well as the extreme value model. In no instance, however, were results on these VaR methods as good as those obtained when the same methods were tested in developed markets. This research highlights noteworthy improvements to value-at-risk estimation efficacy in volatile emerging markets, and also stresses the need for further work into the estimation of value-at-risk in this context.