Jumping CAViAR

Abstract

In this paper, Value-at-Risk (VaR) models that account for intraday-jumps are developed. The VaR is modeled directly as a quantile, the respective model-parameters are estimated by using quantile-regression. In order to analyze the dynamics of the impact of intraday-jumps on the forecasts, different models are developed and evaluated. It is assumed that the underlying time continuous log-price process follows a generic jump diffusion process. Based on this assumption a significant jump-size estimator is used and the jumps are included in the models. The evaluation of the models is done by fitting the model parameters on a high frequency dataset of DAX returns. As an evaluation frame, a data separation approach is used. The empirical results of the models out-of sample performances suggest that the inclusion of jumps does not necessarily improve the backtest results, compared to models without jumps. However, the new models perform better regarding the backtests rejection rate and are less prone to overfitting.

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

JEL Classification: C01, E47, G32