Scale-consistent Value-at-Risk

Returns in financial assets show consistent excess kurtosis and skewness, indicating the presence of large fluctuations not predicted by Gaussian models. In this paper we propose a generalization to the popular RiskMetrics approach to Value-at-Risk. In order to model scale-consistent Valueat-Risk (VaR), we propose a model with a time varying scale parameter and error terms that are truncated Lévy distributed. Lévy flights include a method for scaling up from a single-day volatility to a multi-day volatility. We use this rule to approximate future volatility and estimate Value-at-Risk several days ahead, and compare it to the popular approach, which is a special case of our method. Back-testing results suggest that the inclusion of more sophisticated tail properties and the datadriven scaling rule improves the performance of the VaR model significantly, for short and long time horizons. Our approach is easier to implement and is less time and computer intensive compared to Monte Carlo simulation methods.  2004 Elsevier Inc. All rights reserved.