# Nonparametric Expectile Shortfall Regression for Complex Functional Structure

## TL;DR

This paper introduces a new risk management method using a nonparametric expectile-based shortfall estimator for financial time-series data.

## Contribution

A novel nonparametric expectile shortfall estimator is proposed with theoretical guarantees and practical implementation.

## Key findings

- The estimator's asymptotic properties are established using functional time-series structures.
- The new model shows sensitivity to financial time-series fluctuations and is validated with real and simulated data.
- Comparative analysis shows the new shortfall outperforms the standard one in real data applications.

## Abstract

This paper treats the problem of risk management through a new conditional expected shortfall function. The new risk metric is defined by the expectile as the shortfall threshold. A nonparametric estimator based on the Nadaraya–Watson approach is constructed. The asymptotic property of the constructed estimator is established using a functional time-series structure. We adopt some concentration inequalities to fit this complex structure and to precisely determine the convergence rate of the estimator. The easy implantation of the new risk metric is shown through real and simulated data. Specifically, we show the feasibility of the new model as a risk tool by examining its sensitivity to the fluctuation in financial time-series data. Finally, a comparative study between the new shortfall and the standard one is conducted using real data.