RQ-CAViAR Realized Quantity extended CAViAR Models and their Application.

Abstract

The incorporation of realized quantity measures, based on highfrequency data,
can lead to improvement of forecasts for Value-at-Risk (VaR). Here, VaR models
that incorporate Realized Variance, Realized Semivariance, Jump Variation and the
newly introduced Jump Semivariation, based on an autoregressive quantile regression
model framework, as described by the CAViAR models, are developed, applied
and evaluated. The evaluation of the models is done by fitting the model parameters
on a high frequency dataset of DAX returns. The forecast results are backtested by
the DQ-test and compared to the classic CAViAR models performances based on a
comparative backtest, presented in the form of traffic-light matrices. The empirical
analysis shows that the newly derived realized quantity extended CAViAR models
are not inferior to the already existing CAViAR models described in the literature.
However, no new model consistently outperforms the classic models over all considered
VaR levels. Therefore, it is concluded that the assumption on the functional
relation within the VaR itself is of more importance than the incorporation of additional
information.

Keywords: Value-at-Risk, Quantile Regression, Risk Management, CAViAR, Jump-Diffusion Process, Financial Econometrics

JEL Classification: C01, E47, G32