Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment

Abstract

Expectile-based value-at-risk (EVaR) is a more sensitive measure of the magnitude of extreme losses compared to the conventional quantile-based value-at-risk (VaR). Besides, EVaR is shown to be the only law-invariant, coherent, elicitable risk measure. For these reasons and other advantages, comparing with the existing risk measures (e.g., VaR and ES), EVaR has been recently recommended to use in financial risk management. This article considers nonparametric estimation of EVaR and associated statistical inference for dependent financial time series. The asymptotic properties (strong consistency and weak convergence) of the proposed estimator are investigated in the context of dependence. Monte Carlo simulation studies show that the proposed estimator has desirable finite sample performance. An empirical application to evaluate EVaR of S&P500 returns provides valuable insights for risk assessment in out-of-sample prediction.