What is the value of value-at-risk after all?: A conditional approach using quantile regressions

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and EconomicsIn this Work Project, I propose a new approach to VaR estimation based on quantile regressions which does not require any distributional assumptions. I assume that there exist some state variables that capture persistent changes in risk. This methodology intends to solve the problem of lack of conditionality in VaR models and to capture volatility clustering where existing VaR models currently fail. I compare the out-of-sample performance of existing methods in predicting daily VaR for the S&P 500. I conclude that none of the methodologies developed so far produce satisfactory results in timing unexpected increases in market volatility. Moreover, alternative out-of-sample evaluation techniques yield to opposite results regarding the best VaR model. Nonetheless, in general, the GARCH model outperforms all the remaining models