An evaluation of the adequacy of Lévy and extreme value tail risk estimates

Abstract

Abstract This study investigates the simplicity and adequacy of tail-based risk measures—value-at-risk (VaR) and expected shortfall (ES)—when applied to tail targeting of the extreme value (EV) model. We implement Lévy–VaR and ES risk measures as full density-based alternatives to the generalized Pareto VaR and the generalized Pareto ES of the tail-targeting EV model. Using data on futures contracts of S&P500, FTSE100, DAX, Hang Seng, and Nikkei 225 during the Global Financial Crisis of 2007–2008, we find that the simplicity of tail-based risk management with a tail-targeting EV model is more attractive. However, the performance of EV risk estimates is not necessarily superior to that of full density-based relatively complex Lévy risk estimates, which may not always give us more robust VaR and ES results, making the model inadequate from a practical perspective. There is randomness in the estimation performances under both approaches for different data ranges and coverage levels. Such mixed results imply that banks, financial institutions, and policymakers should find a way to compromise or trade-off between “simplicity” and user-defined “adequacy”.

Keywords

• Lévy–Kintchine-formula
• Value-at-risk
• Expected shortfall
• Generalized extreme value