Markov-Switching GARCH Modelling of Value-at-Risk

This paper proposes an asymmetric Markov regime-switching (MS) GARCH model to estimate value-at-risk (VaR) for both long and short positions. This model improves on existing VaR methods by taking into account both regime change and skewness or leverage effects. The performance of our MS model and single-regime models is compared through an innovative backtesting procedure using daily data for UK and US market stock indices. The findings from exceptions and regulatory-based tests indicate the MS-GARCH specifications clearly outperform other models in estimating the VaR for both long and short FTSE positions and also do quite well for S&P positions. We conclude that ignoring skewness and regime changes has the effect of imposing larger than necessary conservative capital requirements.