Nonparametric conditional autoregressive expectile model via neural network with applications to estimating financial risk

Abstract

The parametric conditional autoregressive expectiles (CARE) models have been developed by [1] to estimate expectiles that can be used to assess value at risk (VaR) and expected shortfall (ES). The challenge lies in parametric CARE modelling is speci cation of a parametric form. To avoid any model misspeci cation, we propose a nonparametric CARE model via neural network. The nonparametric CARE model can be estimated by a classical gradient based nonlinear optimization algorithm. We then apply the nonparametric CARE model to estimating VaR and ES of six stock indices. Empirical results for the new model is competitive with those classical models and parametric CARE models.