Estimating value-at-risk via Markov switching ARCH models – an empirical study on stock index returns

Abstract

This paper estimates the Value-at-Risk (VaR) on returns of stock market indexes including Dow Jones, Nikkei, Frankfurt Commerzbank index, and FTSE via Markov Switching ARCH (SWARCH) models. It is conjectured that structural changes contribute to non-normality in stock return distributions. SWARCH models, which admit parameters based on various states to control structural changes in the estimating periods, may thus help mitigate kurtosis, tail-fatness and skewness problems in estimating VaR. Significant kurtosis and skewness in return distributions of Dow Jones, Nikkei, FCI and FTSE and significant tail-fatness (tail-thinness) in the 1% (5%) region critical probability are documented. Moreover, it is shown that the more generalized SWARCH outshines both ARCH and GARCH in capturing non-normalities with respect to both in- and out-sample VaR violation rate tests.