Evaluating Value-at-Risk Measures in Presence of Long Memory Conditional Volatility

We compare the value-at-risk (VaR) bounds obtained from several models fitted to simulated long memory conditional variance processes. We show that most VaR comparison tests and loss functions may lead to the choice of a misspecified model that produces incorrect risk conditional coverage. The only exception is the test proposed by Christoffersen et al (2001). However, with an opportunity cost loss function, we show that most models satisfy the Basel accord requirements and that the cost of selecting a misspecified model is limited. Therefore, simple models are harmless approximations for the computation of the VaR, both under the users and regulators points of view