A new approach to Value-at-Risk: GARCH-TSLx model with inference

Abstract

In this paper, two-sided Lomax (TSLx) distribution is proposed. The usefulness of proposed distribution is demonstrated in forecasting Value-at-Risk by applying the TSLx distribution to generalized autoregressive conditional heteroscedasticity (GARCH) models. The real data application on Nasdaq-100 index is given to illustrate the performance of GARCH model specified under TSLx innovation distribution against to normal, Student-t and generalized error distributions in terms of the accuracy of VaR forecasts. The backtesting results reveal that the GARCH models specified under TSLx innovation distribution generates the more realistic VaR forecasts than other competitive models for all confidence levels.

Keywords:

• GARCH
• GJR-GARCH
• Lomax distribution
• Value-at-Risk
• volatility