Parametric Value-At-Risk: A Forward Validation Approach For Parameters Estimation

This paper introduces a novel estimation method for parametric Value-at-Risk (VaR) that addresses the risk of misspecification. We incorporate Christoffersen (1998) backtesting framework into the estimation process, as a result the VaR is guaranteed to meet accuracy standards. By framing the estimation as a standard optimization problem, we use the basin-hopping global optimization algorithm to estimate a conditional volatility model and a VaR. We show that our method achieves greater accuracy than the traditional Maximum Likelihood approach. These findings are confirmed by Kupiec unconditional coverage test, Christoffersen conditional coverage test and Christoffersen & Pelletier duration test. Empirical validation is performed on an extensive dataset comprising 46 assets across multiple asset classes over a 30-year period. The results are consistent across various volatility models (e.g., EWMA, GARCH, asymmetric GARCH variants), across sampling periods and distributional assumptions (Normal, Student’s t, and generalized error distributions). The proposed approach provides a robust framework for accurate risk measurement, portfolio optimization, and decision-making under market stress.