Estimation of value-at-risk and expected shortfall based on nonlinear models of return dynamics and extreme value theory

We propose an estimation procedure for value-at-risk (VaR) and expected shortfall (TailVaR) for conditional distributions of a time series of returns on a financial asset. Our approach combines a local polynomial estimator of conditional mean and volatility functions in a conditional heterocedastic autoregressive nonlinear (CHARN) model with Extreme Value Theory for estimating quantiles of the conditional distribution. We investigate the finite sample properties of our method and contrast them with alternatives, including the method recently proposed by McNeil and Frey (2000), in an extensive Monte Carlo study. The method we propose outperforms the estimators currently available in the literature. An evaluation based on backtesting was also performed.