Nonparametric Value-at-Risk via Sieve Estimation

TL;DR

This paper introduces a flexible nonparametric model for estimating Value-at-Risk using sieve estimation, extending theoretical convergence results to ReLU neural networks and evaluating their practical performance through simulations and portfolio risk assessment.

Contribution

It extends nonparametric estimation theory to ReLU neural networks and compares their convergence rates to traditional estimators, providing practical guidance for financial risk modeling.

Findings

ReLU-based sieve estimators have competitive convergence rates.

Monte Carlo simulations illustrate finite sample performance.

Application to portfolio Value-at-Risk demonstrates practical utility.

Abstract

Artificial Neural Networks (ANN) have been employed for a range of modelling and prediction tasks using financial data. However, evidence on their predictive performance, especially for time-series data, has been mixed. Whereas some applications find that ANNs provide better forecasts than more traditional estimation techniques, others find that they barely outperform basic benchmarks. The present article aims to provide guidance as to when the use of ANNs might result in better results in a general setting. We propose a flexible nonparametric model and extend existing theoretical results for the rate of convergence to include the popular Rectified Linear Unit (ReLU) activation function and compare the rate to other nonparametric estimators. Finite sample properties are then studied with the help of Monte-Carlo simulations to provide further guidance. An application to estimate the Value-at-Risk of portfolios of varying sizes is also considered to show the practical implications.