Abstract:
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 volatilityprocessessimultaneously.Astudyofhypotheticalmutualdependenciesbetweenvolatilityandthe 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. Inaddition,theresultsshowthattheestimatedaugmentedmodelshavelowervolatilitypersistence,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-risksforecastsfromourapproach,althoughtheyhaverelativelyhigherfailurerates.Basedonthese results,werecommendtheincorporationofourapproachtoexistingriskmodelingframeworks.Itisbelieved 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.