Using Extreme Value Theory depending on multiple covariates and Machine Learning algorithms to model market risk

This study develops a model that incorporates covariates to the parameters de-scribing the tail of the distribution of asset loss returns. The informative covariates are selected by Machine Learning algorithms. We derive Value-at-Risk depending on covariates and compare the predictive ability with classical risk models such as Historical Simulation and GARCH(1,1). The methodology is applied on two major world stock indics: S&P 500 and FTSE 100. We find that Dow Jones, NASDAQ and VIX are the most influential covariates to describe the left tail behavior for S&P 500. Furthermore, CAC40, AEX and DAX are the top three important covariates to explain the extreme negative returns of FTSE 100. Finally, our proposed models generate low VaR estimates without having more violations than expected