A robust confidence interval of historical Value-at-Risk for small sample

Dominique Guegan (1) , Bertrand Hassani (1) , Kehan Li (1)

1 CES - Centre d'économie de la Sorbonne

Finiteness of sample, as one major sources of uncertainty, has been ignored by the regulators and risk managers domains such as portfolio management, credit risk modelling and finance (or insurance) regulatory capital calculations. To capture this uncertainty, we provide a robust confidence interval (CI) of historical Value-at-Risk (hVaR) for different length of sample. We compute this CI from a saddlepoint approximation of the distribution of hVaR using a bisection search approach. We also suggest a Spectral Stress Value-at-Risk measure based on the CI, as an alternative risk measure for both financial and insurance industries. Finally we perform a stress testing application for the SSVaR.

Mots clés: Uncertainty; Small sample; Value-at-Risk; Asymptotic normality approximation; Saddlepoint approximation; Bisection search approach; Spectral Stress VaR; Stress testing

Domaines: Economies et finances; Gestion et management; Méthodes et statistiques; Probabilités [math.PR]

Dominique Guegan, Bertrand Hassani, Kehan Li. A robust confidence interval of historical Value-at-Risk for small sample. 2016. ⟨halshs-01317391v1⟩