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 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.
Highlights
Risk measurement is one of the most important tasks in financial risk management for banks, corporate treasuries and portfolio management firms as well as other financial institutions and practitioners
The excess kurtosis for all the returns is large and far from zero and the Jacque-Bera tests statistics are very large. This is an indication of non-normality of the return with associated heavy tails, heavy-tailed distributions may be appropriate in modeling the volatility of the returns
There are undesirable consequences associated with inaccurate VaR estimations for banks, accurate forecasting of value-at-risk forms an integral part of decision-making and long-term stability of financial institutions
Summary
Risk measurement is one of the most important tasks in financial risk management for banks, corporate treasuries and portfolio management firms as well as other financial institutions and practitioners. The paper is a contribution to literature on value-at-risk forecasting for emerging markets It would provide further evidence in support of theoretical and empirical studies, which advocate that structural breaks have potentially important implications for estimated GARCH models and value-at-risk forecasts. It can clearly be seen that equation 6 is analogous to the exogenous version of [14], where the exogenous term is represented by the last set of terms These terms move in tandem with volatility by the indirect implications of the asset-return co-movement theory, their absolute values are used to proxy the degree of uncertainties in the exchange rate market in this paper. An upper case letter denotes an endogenous return while lower case letter denotes an exogenous return
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