This paper introduces nonparametric methods for estimating 99.9% operational value-at-risk (OpVaR) and its confidence interval (CI), and demonstrates their applications to US business losses. An attractive feature of these new methods is that there is no need to estimate either the entire heavy-tailed loss distribution or the tail region of the distribution. Furthermore, we provide algorithms that facilitate applied researchers and practitioners in risk management area to implement the sophisticated empirical likelihood ratio (ELR) based methodologies to construct the CI of the true underlying 99.9% OpVaR. In a simulation study, we find that the weighted ELR (WELR) CI estimator is more reliable than the ELR CI estimator. The empirical results show that the nonparametric OpVaR estimates are consistently larger than those of other comparable methods, which provide adequate regulatory capitals, particularly during crises. The findings have implications for regulators, and effective and efficient risk financing.
- Empirical likelihood confidence band
- Loss severity distribution
- Operational risk
- Risk analysis