Monitoring the Value at Risk Over Time in Finance

To appear in Proceedings of the XIVth International Workshop on Intelligent Statistical Quality Control


The value-at-risk (VaR) has become the standard market risk measure since the 1980s and regulators have traditionally used VaR to calculate the capital required for banks to keep.
On the one hand, autoregressive moving average (ARMA) models with generalized autoregressive conditionally heteroscedastic (GARCH) innovations, also termed ARMA-GARCH, have proved to be adequate to describe financial time series that tend not to operate under the assumption of constant conditional variance. On the other hand, control charts have been thoroughly used to detect relevant structural deviations in the process underlying a financial time series.
In this paper, we propose two charts for monitoring the VaR of financial assets assuming that the returns follow a general ARMA-GARCH process. The suggested approach helps investors detect structural breaks in the riskiness of their positions; it also assists them in adjusting their portfolios to comply with regulatory requirements. We believe these charts have the potential to play a crucial role in the swift detection of structural changes in ARMA-GARCH processes and additionally lead to economically profitable investment strategies.