Nonparametric Expectile Regression for Conditional Autoregressive Expected Shortfall Estimation

In this chapter, we estimate the Expected Shortfall (ES) in conditional autoregressive expectile models by using a nonparametric multiple expectile regression via gradient tree boosting. This approach has the advantages generated by the flexibility of not having to rely on data assumptions and avoids the drawbacks and fragilities of a restrictive estimator such as Historical Simulation. We consider distinct specifications for the information sets that produce the ES estimates. The results obtained with simulated and real market data indicate that the proposed approach has good performance, with some distinctions between the specifications.