Value-at-Risk forecasting with different quantile regression models
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- Master's theses (HH) 
Forecasting volatility and Value-at-Risk (VaR) are popular topics of study in econometrical finance. Their popularity can likely be attributed to the statistical challenges related to producing reliable VaR estimates across a wide array of assets and data series. As many financial assets offer unique statistical properties, it has proven to be a difficult task to find a model reliable enough to be considered accepted as the best method. This study focuses on the problem of forecasting volatility and one-day-ahead VaR. The thesis has two main purposes. Firstly, we want to further examine the performance of linear quantile regression models in VaR forecasting against more established models as benchmarks. Secondly, we want to compare the performance between each of the three quantile regression models to see which one performs the best. The three quantile regression models in question are HAR-QR, EWMA-QR and GARCH(1,1) QR. Our findings strongly support the conclusion that quantile regression outperforms the three benchmark models in predicting one-day-ahead VaR for all of the five assets examined. When subjected to coverage tests for both unconditional and conditional coverage each quantile regression delivered perfect unconditional coverage. However, only the HAR-QR model delivered perfect conditional coverage and thus performed the best of the three models. The benchmarks models RiskMetrics, GARCH(1,1) and Historical Simulation showed particular problems with estimating the left tail quantiles of the distribution. The study shows that compared to the QR approach, these models fail to capture time variant volatility and the negative skewness and leptokurtosis that is present in the assets return distributions.