Capturing the intrinsic uncertainty of the VaR: Spectrum representation of a saddlepoint approximation for an estimator of the VaR

Though risk measurement is the core of most regulatory document, in both financial and insurance industries, risk managers and regulators pay little attention to the random behaviour of risk measures. To address this uncertainty, we provide a novel way to build a robust parametric confidence interval (CI) of Value-at-Risk (VaR) for different lengths of samples. We compute this CI from a saddlepoint approximation of the distribution of an estimator of VaR. Based on the CI, we create a spectrum representation that represents an area that we use to define a risk measure. We apply this methodology to risk management and stress testing providing an indicator of threats caused by events uncaptured in the traditional VaR methodology which can lead to dramatic failures