An Empirical Comparison among VaR Models and Time Rules with Elliptical and Stable Distributed Returns

This paper compares and investigates the impact of different VaR models with conditional elliptical and stable distributed returns. In particular, we analyze some non-Gaussian VaR models and we discuss the applicability of some temporal aggregation rules. Thus, we propose and examine the performance of several VaR models: (i) an EWMA model with Student's t conditional distributions, (ii) a stable sub-Gaussian model, (iii) a stable asymmetric model. All models are subjected to backtest on out-of-sample data in order to assess their forecasting power and to show how the associated aggregation rules are performed in practice.