The Use of Mutual Information to Improve Value-at-Risk Forecasts for Exchange Rates

In this paper, we show a simple but novel approach in an attempt to improve value-at-risk forecasts. We use mutually dependent covariate returns to create exogenous break variables and jointly use the variables to augment GARCH models to account for time-variations and breaks in the unconditional volatility processes simultaneously. A study of hypothetical mutual dependencies between volatility and the covariates is first carried out to investigate the levels of the shared mutual information among the variables before using the augmented models to forecast 1% and 5% value-at-risks. The results provide evidence of some substantial exchange of information between volatility and the lagged exogenous covariates. In addition, the results show that the estimated augmented models have lower volatility persistence, reduced information leakages, and improved explanatory powers. Furthermore, there is evidence that our approach leads to fewer violations, improved 1% value-at-risk forecasts, and optimal daily capital requirements for all the models. There is, however evidence of relative superiority of the majority of the models for the 5% value-at-risks forecasts from our approach, although they have relatively higher failure rates. Based on these results, we recommend the incorporation of our approach to existing risk modeling frameworks. It is believed that such models may lead to fewer bank failures, expose banks to optimal market risks, and assist them in computing optimal regulatory capital requirements and minimize penalties from regulators.