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

Dominique Guegan (), Bertrand K. Hassani () and Kehan Li ()
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Dominique Guegan: Centre d'Economie de la Sorbonne, https://cv.archives-ouvertes.fr/dominique-guegan
Bertrand K. Hassani: Grupo Santander et Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.univ-paris1.fr
Kehan Li: Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.univ-paris1.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: 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

Keywords: Value-at-Risk; Small sample; Uncertainty; Asymptotic normality approximation; Saddlepoint approximation; Bisection search approach; Spectral Stress VaR; Stress testing (search for similar items in EconPapers)
JEL-codes: C14 D81 G28 G32 (search for similar items in EconPapers)
Date: 2016-04
New Economics Papers: this item is included in nep-ore and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16034

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