Extreme value modelling for forecasting market crisis impacts

Abstract

This article introduces a new approach for estimating Value at Risk (VaR), which is then used to show the likelihood of the impacts of the current financial crisis. A commonly used two-stage approach is taken, by combining a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) volatility model with a novel extreme value mixture model for the innovations. The proposed mixture model permits any distribution function for the main mode of the innovations, with the very flexible Generalized Pareto Distribution (GPD) for the upper and lower tails. A major advance with the mixture model is that it overcomes the problems with threshold choice in traditional methods as it is treated as a parameter in the model to be estimated. The model describes the tail distribution of both the losses and gains simultaneously, which is natural for financial applications. As the threshold is treated as a parameter, the uncertainty from its estimation is accounted for, which is a challenging and often overlooked problem in traditional approaches. The model is shown to be sufficiently flexible that it can be directly applied to reliably estimate the likelihood of impact of the financial crisis on stock and index returns.