The Spectral Stress VaR (SSVaR)

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

1 CES - Centre d'économie de la Sorbonne

One of the key lessons of the crisis which began in 2007 has been the need to strengthen the risk coverage of the capital framework. In response, the Basel Committee in July 2009 completed a number of critical reforms to the Basel II framework which will raise capital requirements for the trading book and complex securitisation exposures, a major source of losses for many international active banks. One of the reforms is to introduce a stressed value-at-risk (VaR) capital requirement based on a continuous 12-month period of significant financial stress (Basel III (2011) [1]. However the Basel framework does not specify a model to calculate the stressed VaR and leaves it up to the banks to develop an appropriate internal model to capture material risks they face. Consequently we propose a forward stress risk measure “spectral stress VaR” (SSVaR) as an implementation model of stressed VaR, by exploiting the asymptotic normality property of the distribution of estimator of VaR p. In particular to allow SSVaR incorporating the tail structure information we perform the spectral analysis to build it. Using a data set composed of operational risk factors we fit a panel of distributions to construct the SSVaR in order to stress it. Additionally we show how the SSVaR can be an indicator regarding the inner model robustness for the bank.

Mots clés: value at risk; asymptotic theory; distribution; spectral analysis; stress; risk measure; regulation

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

Dominique Guegan, Bertrand K. Hassani, Kehan Li. The Spectral Stress VaR (SSVaR). 2015. ⟨halshs-01169537⟩