Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)

TL;DR

This paper introduces new dynamic models for Expected Shortfall and Value-at-Risk, addressing modeling challenges and demonstrating improved forecasting performance over traditional methods using international equity data.

Contribution

It proposes the first joint modeling approach for ES and VaR that overcomes elicitability issues, with estimation methods and empirical validation.

Findings

Proposed models outperform GARCH and rolling window models in forecasting accuracy.

Simulation studies confirm good finite-sample properties of the estimation methods.

Application to international equity indices demonstrates practical effectiveness.

Abstract

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of "elicitability" for ES by jointly modelling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES-VaR models outperform forecasts based on GARCH or rolling window models.