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Rachida Hennani and Michel Terraza
''Contributions of a noisy chaotic model to the stressed Value-at-Risk''
( 2015, Vol. 35 No.2 )
The weaknesses of current Value-at-Risk (VaR) measure led the Basel Committee to revise the Basel II market risk framework. A stressed VaR measure is introduced to incorporate the violent behaviour of financial markets during crisis periods. This requirement allows the pro-cyclicality of the current VaR to be removed. However, this solution does not solve the problem related to the VaR estimation, including the choice of an appropriate model in a parametric approach. The forecasts of those models must comply with the assumptions of unconditional coverage and independence. In this paper, we evaluate the contribution of a noisy chaotic model for estimating the VaR measure in a crisis period. The simultaneous consideration of heteroskedastic and chaotic structures leads to a better forecast of the returns (Kyrtsou and Terraza (2010)). This clarification relative to the GARCH (1,1) model is used in this paper for predicting the stressed VaR of a portfolio built according to the mean-Gini criterion. The forecasting exercise, evaluated by backtesting tests, shows an outperformance of the Mackey-Glass-GARCH (1,1) model.
Keywords: Value-at-risk, Mackey-Glass model, GARCH, backtesting tests, Mean-Gini portfolio, dynamical and chaotic systems
JEL: C1 - Econometric and Statistical Methods: General
Manuscript Received : Feb 06 2014 Manuscript Accepted : Jun 01 2015

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